In my experience, moving is a really, really big deal. I've lost entire firefights because I had to stand there and reload instead of being able to move + shoot or move + suppress. Unless you're playing all 0% raids, timers do actually matter, you often have to move towards the objective while shooting every turn, and the difference between a white reload and a green reload is easily one of the deciding factors in battle. I often find myself going "crap, I didn't build an autoloader?! That would gone SO much smoother." I completely disagree with autoloaders being situational, at least on classes that can use 2+ ammo per turn.As long as there are eligible targets in range, a white reload is just as good as a green one - and, given the gunner's tendency to empty their magazines in a jiffy, it's not unlikely that their first reload *will* occur while there are still good targets in range, or between firefights, where a free reload is even less useful. In my experience, the value of an autoloader for a gunner lies in being able to move on an empty magazine (instead of wasting the first action on reloading) before using a costly special attack, at least in the first encounter- but that value evaporates quickly, is very situational and therefore not easily quantifiable.
One very practical example is when you go sharpshooting to kill relays from squad sight. One basic autoloader saves you from having to reload at all (assuming you can kill the relay in 6 shots, which is pretty reasonable), and that one turn often does make a difference between whether you get it done or whether the enemy happens to bump into you. You'd have to have an elite magazine to come up with the same effect.
Another practical example is the assault class. One basic autoloader should save you from having to reload in a practical battle (like a retal, or other small'ish mission that isn't swarming). I find that 4 shots isn't ever enough and when you are constantly trying to move up to get into a better position, it's a really bad thing if you find you have to reload instead of being able to get that flank shot.
Timers make autoloaders extremely relevant and to me one of the most powerful and desirable weapon mods. If I just had to recommend a quick and dirty 3 mod layout without knowing any details, it would look like scope - autoloader - expanded magazine. You can do better knowing more details, but I think you might be surprised how strong that setup is for anyone who actually fires with their primary weapon.