I'm afraid it's more than that.
First and foremost, there are no fundamental reasons why ships cannot be extended forever and a day. Unfortunately, doing so incurs costs that are either comparable with or more than the cost of a new build ship. A few reasons why -
1. Weight growth. All ships incur weight growth through-life and quite often vertical centre of gravity increase as well. This affects both stability (weight and VCG) and structural strength (weight only). While some elements of growth can be accounted for fairly easily (oh look, that wasn't there when she was built), others cannot and include things like redundant cabling left in the ship, paint, minor seatings etc. These can add up to several hundred tonnes on even a frigate sized ship (there are type T23s running round with well over 10% increase in weight already!). Stability certificates are being brought more in line with IMO legislation and in terms of safety cases are being made ALARP which essentially means that over time standards will gradually become more onerous.
The only way to recover stability is either to add ballast (and we're talking in hundreds of tonnes of lead here) or remove all the weight (which essentially means gutting the ship, blasting back to bare metal and then reinstalling only what the latest mod state says should be there. This involves lots of manpower, which is very expensive and limited in application (ie you can only get so many folk on a ship at the one time), so the job takes longer.
Adding lots of ballast just adds to your structural strength problem and because the ship sits lower in the oggin makes your damaged stability worse - you are in effect, chasing your tail.
Structural strength itself requires adding lots of additional metal to the upper decks and the keel to bear the increased load (weight, buoyancy and wave loading), which again is expensive, adds weight and doesn't help stability. Tail chase again.....
2. Corrosion of ships hull. Again, can be overcome by replating, but becomes progressively harder to do as you chase sound structure, reducing availability and costing more than new fabrication. All the museum ships you quote require regular dockings (see Intrepid recently and Alabama a few years ago with extensive replating) and none of these are certificated to go to sea. they can get away with dockings every ten years or more, but are not expected to be subjected to wave loading, hence lower standard required.
3. System obsolescence - another big killer. Again, huge amount of cost involved. You can't actually extend gas turbines indefinitely either, nor missile motors, or electrical cabling etc. You have to rip it all out and fit new - which may be a different standard to that which was built, bringing different problems in safety world.
After all that, you've got a phenominally expensive platform, which still has simlar performance to when it was built, which may be much less than required now. Better all round to spend on new and overcome the nasties identified above at design rather than try and bodge them.