STAR, the system we're advocating, solves a lot of these issues though. Score voting is "like" approval voting but with more precision (really approval is just the binary version of score). STAR05 is often suggested because experimentation shows that it has enough expressiveness to generate good winners but is simple. You can always add more expressiveness by increasing the range in which you can score candidates, but there's diminishing returns as you increase it and added complexity (I don't think people will have a problem rating 0-10 though since we actually do that a lot).
I cannot think of any way that IRV beats out STAR. In STAR's worst case scenario (1-sided strategy) it still has a VSE equal to IRV's best scenario (100% honest). Any more honesty that people have in STAR just improves peoples' satisfaction. This is actually one of the main arguments of cardinal systems over ordinal systems (e.g. STAR vs RP/IRV).
If you're really into the ordinal camp, I'd also strongly encourage you to look into Ranked Pairs. The satisfaction is A LOT higher than IRV does. On the ballot side it is no different than what the voter sees in IRV (really this is fairly consistent for ordinal systems, by definition).
But I want to stress that STAR and Approval are not equivalent. I also want to stress that scoring is an extremely familiar concept to most people. "Rate this drive out of 5 stars." "On a scale of 1 to 10 how would you rate..." etc. So I'd argue that STAR is fairly expressive (which seems to be your major complaint) and is a simple and easy concept for voters to understand (since they are already familiar with it).
I'm a co-inventor of STAR voting. I explain it as, STAR voting is score voting on a 0-5 scale followed by an automatic ("instant") top two runoff. Whereas approval voting is score voting on a 0-1 binary scale. STAR voting performs a tiny bit better in computer simulations of voter satisfaction, but approval voting has the practical benefit of being super simple and requiring no voting machine upgrades. Both are superior to IRV.
Here's the first email I received from Mark Frohnmayer where he discussed STAR voting, following my speaking at his conference at University of Oregon, that gave birth to it. :)
https://twitter.com/ClayShentrup/status/1278118075972202496
STAR sounds very reasonable. And yeah, I'm definitely open to ordinal systems besides IRV. I guess my argument is about letting the perfect be the enemy of the good (which is of course the whole point of voting systems to begin with). I'd consider IRV or MMP vastly better than FPTP, and something like STAR or Ranked Pairs only slightly better than that. Which is a good example of a preference that STAR would be good for expressing :P
> I guess my argument is about letting the perfect be the enemy of the good
I see this as more when you're creating something. Like if you're writing software if it is good enough then don't continue if you have other pressing matters. Essentially this saying is about Pareto.
But when you already have things invented and you're just selecting things, this saying doesn't apply. We have 3 options: option 1 sucks, option 2 is meh, option 3 is pretty good. Which do you choose? It is pretty obvious that you should choose option 3. There's no other conditions on this problem. You don't have to spend more resources to get option 3. Option 3 is just objectively better, so why not pick it?
And if you think I'm exaggerating, I'll note that IRV is a 6% VSE improvement on plurality. STAR and RP are both 15% improvements on plurality. This is part of why people are frustrated. There's options that are objectively better, so why pick the worse one? And it isn't like they are differing in "betterness" by small amounts, we're talking about a pretty big amount!
You're calling 6% "vastly better" so doesn't that make 15% "astronomically better?"
I cannot think of any way that IRV beats out STAR. In STAR's worst case scenario (1-sided strategy) it still has a VSE equal to IRV's best scenario (100% honest). Any more honesty that people have in STAR just improves peoples' satisfaction. This is actually one of the main arguments of cardinal systems over ordinal systems (e.g. STAR vs RP/IRV).
If you're really into the ordinal camp, I'd also strongly encourage you to look into Ranked Pairs. The satisfaction is A LOT higher than IRV does. On the ballot side it is no different than what the voter sees in IRV (really this is fairly consistent for ordinal systems, by definition).
But I want to stress that STAR and Approval are not equivalent. I also want to stress that scoring is an extremely familiar concept to most people. "Rate this drive out of 5 stars." "On a scale of 1 to 10 how would you rate..." etc. So I'd argue that STAR is fairly expressive (which seems to be your major complaint) and is a simple and easy concept for voters to understand (since they are already familiar with it).