Wouldn't various A/F ratio problems such as vacuum leaks, low fuel pressure or clogged injectors cause a constant adjustment to fuel trims, first via STFT and then to LTFT? For example, if there is a air / vacuum leak significant enough to cause noticable idle problems wouldn't that cause a more or less constant attempt by the computer to compensate by adding fuel, even at idle?
You have hit the nail on the head.
When the car is in closed loop, this part is important, the fuel trims reflect the current A/F ratio. When a vacuum leak develops, first the car will compensate withe the sort term fuel trims. When the STFT stay high long enough (every car is different) they will cause the LTFT to drift.
Current fuel systems are so tight that inducing even the slightest leak will be reflected first by the STFT and then by the LTFT even at idle. This is actually a great test to see if a car is in fuel control. Induce a vacuum leak while watching the fuel trims they should climb. Then using propane, induce some in to the system and the fuel trims should fall.
It does to a certain point but it has to be limited to avoid engine damage.
ECM first set it's base value let say 3.5ms. This is received from signals such Airmass, TPS, crankshaft position sensor etc. When both the long and short term fuel trim sit in they mid value 0% the injection pulse width is unmodified.
Changing conditions result in a different calculated engine load, the 3.5 ms base injection duration will reduce or increase. Oxygen sensor (O2) will fine tune this value depending on the various conditions through the STFT (short term fuel trim).
Most engines are design to run at stoichiometric ratio 14.7:1, that is 14.7 part of air to 1 part of fuel. This is the best ratio for clean emissions, one of the reasons why STFT even exist is to compensate for engine wear, altitude, climate and to a certain point problems in the engine.
Imagine the software in the ECM is design to set a min. base value of 2.5ms and maximum value of 4.5ms. If there is problem in the engine that will cause the injection value to either increase or decrease beyond this threshold a fault code 'mixture adaption value out range' will be logged. This is to simply prevent drive ability problems and engine damage.
You can't just keep on dumping more and more fuel if you have a vacuum leak for example. To much fuel will create bore wash (dry cylinder walls) which will lead to excessive oil consumption, residual fuel will ignite inside the CAT (catalytic converter) melting it down. This is already a case if you drive with a normal problematic engine for a period of time.
Hope that helps.