Except that C defines the way nearly everything everywhere passes function parameters over registers. Not C's fault, but still a thing affecting everyone that doesn't write C, as C doesn't even try to be a good ABI, because it wasn't meant to be.
How does a language "try to be a good ABI"? An example of such a language would help.
An ABI doesn't need to be a language. In fact, I'd say that makes it worse, as now you'd have a potentially conflicting goal, wanting to make it nicer for the language itself, possibly at the cost of making for a worse ABI.
But one could do well with not having varying width integers (looking especially at you, "long"), having a defined structure layout, and one (primary) calling convention per architecture (it not being the absolute best if goals change would be fine, as it'd only be used to talk between different languages, and that usually doesn't happen with such a frequency that a couple nanoseconds hurt). Sure, you'd still end up with some variance, but it'd be a lot easier to work with, and it'd be pretty hard to reach the count of 176 ABIs of C.
edit: ..and just not defining things that aren't actually related to ABI (or may need to change), i.e. intmax_t
I don't think that that is correct. Sure, your C implementation defines which params go into which register in a certain way, but other C implementations define the same thing in a different way.