IIRC Oracle does support this and calls it a skip-scan. If the first column in the index is not very selective this can be very efficient, though if the first column is good in terms of selectivity then a skip-scan will be very inefficient and the DB might as well just scan the whole index. Given that a good choice of index usually has a fairly selective column as its first, and that unless storage space is very cramped you are likely better off just defining an extra index without the column that you want to not touch in some queries, this means that a skip-scan isn't helpful as often as one might think which is one of the reasons DB engine maintainers give for not spending time implementing and maintaining the feature.
There are some use cases where having the option to skip-scan is definitely a significant bonus, but they are rare enough that I understand why most engine maintainers have not implemented them.
I can think of several cases where it would have been nice to have, sometimes "good enough" for a particular read pattern is better than additional write overhead etc.
Of course an obvious counter is to implement it as an optional feature only used when explicitly requested by a query hint, with the counter counter being "is it worth the implementation effort given how rarely it will get used in that case?".
Oracle's developers were seated by the benefits, other database developers have not been.
There are ways to "emulate" the behaviour using CTEs to gain the expected benefit in at least some cases, but I've not experimented with this myself so can't speak for how well it works in practise, or if the extra legwork makes queries too convoluted to be easily maintained (or understood easily at all be future maintainers).
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[1] noting that query planners do not strive to produce the best query plan, that is a Turing complete problem in many cases, instead trying to make a good enough choice in a reasonable amount of time
I maintain a couple fairly large db deployments totalling around 100 machines, and it's always fun to see how query planner jitter affects things on a larger scale.
https://www.postgresql.org/docs/current/indexes-multicolumn....
Also worth noting that for very complex workloads that need to support arbitrary subsets of equality matches over columns, a Bloom filter might work best:
Maybe eventually PG will also get index skip scans for btrees, which could allow for arbitrary columns searches in the btree; but we're not there yet by a large margin.
https://dev.mysql.com/doc/refman/8.0/en/range-optimization.h...
This means the order does matter
Sorry my comment is not semantically accurate enough for you.