On the subject of RPG elements

[Schultzy]

And what do you suppose that "efficiency" translated to in gameplay terms in SH3?

This may well be the crux of the matter.
I don't think anyone would object to a well crafted, well reasoned promotion based system whereby experience translates to better performance.

After five patrols and many hours drill, I really do hope that my Torpedomate can now do his job so well, that it's almost second nature, and that as a consequence, the torpedos load 1 or 2 seconds faster.
I don't mind the idea that my Chief Engineer knows the limits of his boat because he's been to sea in her so many times, and that his inate knowledge adds a few feet of depth before crush is reached.

So, while perhaps it's engaging in semantics, it's no less valid to say, that as a player, seeing (for sake of argument) a pop up box offering the player a level two soup upgrade: crew don't tire as quickly, the suspension of disbelief is eroded.
It sounds and feels more like a we're playing a game, which we don't want to be reminded of.

have any better ideas than what's being done in SH5.

I'm not entirely sure it's a case of a better idea being needed, rather that the current idea be better implemented. Make the levelling up less overt. Give it context.