To put it another way: given a (sufficiently large) set of [0,1] score votes, you can generate a set of approval votes that give a very good estimate for the score voting results by mapping each score vote to an approval vote by randomly picking a number in [0,1) for each vote and marking options scored above that threshold. Handwaving a bit, this implies that at scale approval voting and arbitrary-precision score voting give the same results with pretty good probability.
Now, score voting with arbitrary precision pretty clearly conveys more information than ranked choice! You can extract an RCV from a score vote directly, but this loses substantial information about how far apart the options were rated. Conversely, if you extract a score vote from an RCV, you ... well, you can get something like Borda count. For other RCV aggregation algorithms a score vote extraction is not quite as clean, but it's substantially less clear whether the information "lost" is real or an accidental artifact of the RCV itself. Certainly you can argue all day over the merits of Borda count and variants vs other IRV aggregation algorithms, but then score voting with arbitrary precision not only strictly dominates Borda count, but also is clearly conveying additional information about degree of preference on top of that which is obviously useful and not encoded in ranked choice votes at all!
Bonus: a surprisingly large number of decisions are dominated by no more than three viable choices that are clearly preferred over all others. When selecting for among three options, there are seven unique approval votes (the all marked/unmarked votes, expressing no preference, are equivalent), and only six ranked unique choice votes. It should be pretty clear that RCV and approval don't convey equivalent information in this case!
