if my 750W PSU had aged to the point where it could only output 650W
Whoa!!! Stop there!
There seems to be a lot of confusion here about how efficiency effects output. The reality is, it really doesn't in any significant manner.
Assuming a capable supply, if the computer (motherboard, RAM, CPU, GPU, drives attached devices, etc.) demands 300W, the power supply is going to deliver 300W regardless if the supply 90% efficient, 80% efficient or even 70% efficient.
The difference is what the supplies demand
from the wall.
With a 300W load the
90% supply will demand ~333W (333 x .9 = 299.7).
80% supply will demand ~375W (375 x .8 = 300).
70% supply will demand ~400W (400 x .7 = 301).
That extra 33, 75 and 100W will be consumed by the power supply but wasted in the form of heat. Regardless, each supply will still deliver to the computer the 300W it is demanding.
Also, note that power supplies lose capacity over time due to aging that is NOT a result in a decrease in efficiency. But the loss in power capacity is no where near the scenario you just described. 650W down from 750W would be almost a 15% loss in capacity. No way that would happen simply due to age. There would have to be some other malfunction or failing component to cause that. More typical would be ~5% loss in capacity. That is, a 1/2 decent 750W supply may lose ~37 to 40W capacity over time. Not 100W. It must be noted that 1/2 way decent power supplies already are designed to compensate for some aging. So do ALL PSU calculators when recommending sizes. And users should take aging into consideration when purchasing a supply too.
Or is the question too hard to answer altogether with unpredictable behaviour depending on design?
It is too hard to answer because of all the unknown variables. But unpredictable "behavior" is not one of them. We know how supplies will behave in essentially every scenario one may be operated in. The problem is, we don't know which that scenario that will be.
For example, you didn't tell us what hardware this supply is supporting. We don't know the manufacturer or model number of the supply. We don't know the average ambient temperature it will be operated in. We don't know how clean the power the supply is consuming. We don't know how old this supply is or the type of loads it has had to support. We don't know how many hours per day it has been used.
If you are asking if you should replace your supply
just because it is X number of years old, the answer is, "no". But that answer is based on a few assumptions, including, is it a quality PSU, was it sized correctly to begin with, did the user provide adequate cooling throughout its life?