the guns on a fighter plane/starship

I see it as analogies of naval gun barrels needing replacement except you would not hand those up on the wardroom wall.
The BL 14-inch Mk VII naval gun mounted on British Battleships like King George the Fifth and the Prince of Wales could fire around 350 shots at full charge before it was recommended that the barrels were replaced, other nations using different gun technologies could fire different amounts that’s part of why denial of the shipyards at St Nazarie through Operation Chariot which stopped the Germans refitting Tirpitz was important.

I think in DS-9 they could have recycled those weapons parts if they wanted by Sisko felt than generating an Esprit de Corps was more important. Although it’s also possible with the stripped back design of the Defiant it may not have had the same industrial replicator capacity a Galaxy or Excelsior class, and this may have been done off ship,

Both would make sense. As an 'escort' the Defiant wasn't designed for long range exploration, something that would appear to be backed up by the lack of crew facilities normally seen on even small Federation Starships. This in turn may also explain why Starfleet was quite happy to allow the Defiant to be pulled out of storage for deployment on DS9.

My comment about the age of the power cells was actually based on the assumption that the Defiant would be overhauled while docked to DS9 by Chief O'Brian. It's made very clear that this was one of the functions of the station and duties O'Brian had from the moment Starfleet took over the station. For some reason I failed to make the connection that one main reason for this was most likely that the Defiants size and design probably omitted some of the 'industrial' equipment found on larger ships.

This aspect of the Defiant is probably why the design wasn't put into production prior to the Dominion War, or possibly earlier during the war with the Klingons. While it could be argued that the problems with the Defiant being overpowered was the main reason. That a fairly small crew on DS9 were able to not only overcome those problems but unleash the full potential of the design in a very short amount of time would indicate that the original design team should have been able to do the same.
More likely is that Starfleet was still fixated on the 'exploration' aspect of their function. And as such didn't see the need for a small ship that lacked the range and flexibility of something bigger, such as the Sabre class which had the same crew compliment, and would be dependent on a base for repair and maintenance.
A mixture of actual combat experience and the missions the Defiant successfully undertook even before any serious combat took place must have shown that these ships had far more potential and flexibility than anticipated. The design may not have been ideal for exploration but was capable of performing such missions if needed. It would also be ideal as an armed courier or transport or perform diplomatic missions that didn't require a major ship. Indeed one would assume that the Defiant class ended up being engaged in such tasks after the war helping free up larger designs for other missions - In TNG episode 'Tin Man' Captain DeSoto of the USS Hood*, an Excelsior class ship, claimed that he spent most of his time flying from one star base to another while the big ships (meaning the Galaxy class Enterprise D) got to do all the fun stuff. While this was said with a smile there is probably some truth to the claim. Meaning that a large ship was being tied up on duties that could have been carried out by something smaller. You certainly don't need an Excelsior class ship to ferry one person around*.

(*The USS Hood was first seen, and her Captain mentioned, in Encounter at Farpoint. This was the ship Riker was first officer on prior to serving on the Enterprise. Interestingly in both of her appearances she is only meeting up with the Enterprise to drop off personal. Meaning that she was basically a glorified shuttlecraft on both occasions.)

It does seem likely that the pulse phasers placed a much higher strain on the power cells than traditional phaser array. It seems that standard phasers usually required a two second blast to overload the shields of a target to damage the hull or systems. The Defiant's pulse phasers were firing in quarter to half second blasts and capable of not only overloading the shields but potentially obliterating a target entirely. We also saw the difference in damage potential from First Contact, where the Defiant's strafing run against a Borg cube caused as such damage per 'bolt' as a photon torpedo.
So it is highly likely that the power cells were being charged and drained at a considerably higher rate than they had been designed for. It's also telling that redirecting all power from the phasers, even outside combat, considerably increased the Defiant's top speed and required at least a day to fully recharge to allow the weapons to be used again. It certainly gives some idea as to how much energy those cells must contain, and therefore how powerful the pulse phasers must be to warrant that kind of power storage.

Although none of this seems to have much to do with the original question, it does actually show how technology effects the design of combat vehicles and how such ships could/can be used. In Trek much of this is clearly unintentional, but still manages to remain logical and consistent with Trek technology and the cultures of those designing ships. These may seem like minor matters creatively speaking. But one of the oft overlooked, yet important, aspects of creating a fictional world is in developing a 'realistic' and logical background for that world. One which not matter how different things work there is still an understandable logic to them. Even Terry Prachetts Discworld has its own logic and laws which characters or technology have to conform to. It's one of the reasons that, as absurd as the Discworld sounds, it works very very well as a setting.

3. It was a Star Trek series, and the plot called for the main characters to do something absolutely heroic in nature using minimal equipment.

I imagine that somehow, O'Brian's repairs involved at least a solid case load of space duct tape.

The Battle of Wolf 359 was in 2366. USS Defiant was launched in 2370 and assigned to DS9 in 2371. So it took about 4 years to design and build her.

After Wolf 359, it was likely they had a version of a brain storm session with ships. They take a bunch of ideas and concepts and see which which one have merit.

Likely Defiant was a bit of a Frankenstine. Take some off the shelf phaser cannons and build a ship around it using whatever you can get easily laying around the shipyard. Being that it is a very small ship by the standards of the day, and a ultra utilitarian design, it was a fast ship to build, as much as a proof of concept as anything.

Once it was launched in 2370, they found out about the limits to the rev A design. When that happened, it was likely shuffled to the back burner. The design had promise, but needed bugs worked out. However, there were other designs that showed more promise when viewed through the sensibilities of the day. So when Sisko asked about an escort for the station, it did make sense. Likely there were designs for fixes that were already in the works and half complete, just needed final tweaks and then built and installed.

DS9 is a pretty good place to do that sort of work. You have a large star base with the manpower and industrial capabilities plus nearby Bajor with its resources. Everything you need to finish the half done designs for the fixes and get them installed. Add to that Bajorain engineers had a knack for figuring out how to make stuff work because of what they experienced in the occupation.

as I recall, the biggest complaint was that it was overpowered - which would mean that it probably cut into the safety margins of some combination of control systems, structural integrity fields, and inertial dampeners.

I would imagine that some of the sentiment that led to the project getting back-burnered was "that's a warship. the federation doesn't do warships" from the diplomatic ranks.

which would mean that a good percentage of what O'brien had up his sleeve was probably was a willingness to reduce safety margins a little bit - or even put in a couple lines of code that throttled back the engines unless the helm specifically asked for emergency power.

That works for just about any kind of fiction.

Even if you say "this work is taking place in the real world", you're setting the rule that "anything which wouldn't exist in real life doesn't exist here without a *very* good explanation".

Yes DS-9 was not a Space Dock or a Starbase, as Terak Nor it was a relatively minor loading station above one of Cardassias most marginal occupied world, I doubt it was equipped with too much repair equipment really. It’s is more a port like Brixham than Portsmouth harbour.