I can't say I've had much issue with this in postgres, but even still, this is easily worked around by having a pkey/cluster key of a monotomically increasing int--which is useful for other things such as data migrations, as you can pick defined start and end targets without worrying about new things being inserted in between.
Pg does not cluster, so the only impact of a uuid is that you’re inserting in a random location location of the index, which is not great but not the end of the world (probably).
InnoDB clusters on the PK by default, so when you're inserting a UUID you're not only inserting in the middle of the index (on average) you're also inserting in the middle of the table.
And I don't know how much the on-disk storage has been optimised for this sort of things, but if the answer is "not" and sparse pages are not really a thing, you might need to rewrite half the table in order to do so.
