If you pull that off, it's because you're just plain better at the game than I am anyway (or you had great luck with the RNG/I had bad luck), and you'd have finished in fewer turns if you had used those resources.
Not all advantages will be reflected by turncount, though, and I certainly don't like the implication that no other metric has significance. Is it impossible to improve on a LTC strategy in Talons Alight because any success is a 7-turn? Surely not!
The main thing for me is just that it feels like it doesn't make a lot of sense from either a gameplay or a character perspective.
By playing for Funds, you're giving up short-term advantages in return for long-term flexibility, both in and out of universe. Perhaps you give the first Speedwings to Alan while I hold it in reserve; later we find that Lance is one Speedwings short of some important ORKO. I can still get that KO, and if I was able to maintain parity in other departments despite my weaker Alan, then my skills are demonstrably superior.
Now, in order to maximize Funds, you have to never use that Speedwings. Out of universe, that's fine, because it means you have beaten the Never Use That Speedwings Challenge. In-universe, who is to say that you know ahead of time when the final battle will be, and what you'll need to win it? It's best to hold your resources until emergencies, so that when emergencies inevitably happen, you are prepared.
By playing for EXP, you are again maximizing endgame power, by ensuring that your team gains as many levels as possible. In theory, anyway - I agree that deployment limitations and suchlike mean that theory does not always apply to practice, here. You also get some flexibility and whatnot, by having more viable characters to choose from. But a better reason in-universe is that you're supposed to be commanding an army, not picking statblocks from a list. You might only bring a third of the party to deal with the Evil Overlord, but the other two-thirds still need to be ready to hold off his Army of Darkness. Leave some poor kid green the entire war just because the only thing she brings to battle is courage, and she might be going home on a shield. Meanwhile, your top fighters are not tireless, and having them in the thick of battle all day every day is just asking for trouble. Just because only one game has S Drinks doesn't mean no one in the others feels fatigue!
All that said, it is my belief that the primary justification of the EXP Ranking is "discourages people from relying on a small, overlevelled team", and to be perfectly honest I am OK with that. I personally find strategies like "dump a hojillion BEXP on this unit, have them solo chapters" to be repugnant.
And then FE5 has the most coherent system since all it asks of you is to do things that make sense (recruit everyone and get low turn counts), though it has the glaring flaw that to get the best rank you'll have to warp skip a ton of maps.
But those limited criteria are exactly my issue with it! Particularly since I tend to view "recruit all units and keep them alive" as an implicit goal of any non-Shadow Dragon playthrough. (If I ever play FE5... well, I'll recruit everyone at least once. After that I may consider making an exception or two.) That leaves FE5's ranking system with one true goal, and a FE5 ranking run as absurdly overspecialized. In a FE7 ranking run, you're challenged to utilize your resources to achieve multiple conflicting goals as best as possible, to come up with a plan that can fulfill all the requirements and not merely one. In FE5, you're striving single-minded after a solitary goal. Which allows you to achieve laserlike focus, sure, but such single-minded obsession does not interest me.
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I don't like this duchy. Now, it's an adventurer.