They actually do work like that in Postgres, and in general for secondary indices. Like, I'm positive there are some btree variants that deal with duplicate data better, at the cost of slower writes or more locking (just an example), but we're talking about normal btrees.
In his book "An Introduction to Database Systems", DB2 Architect CJ Date describes an index design that compresses indexes of similar strings. So if entries in the index block start with the same first few letters, the first entry has the complete string, and subsequent entries use the format: <count-of-matching-characters> <remaining-characters-that-are-different-than-previous>. The algorithm burns some CPU to conserve I/O.
For example:
0 let
3 ter
6 s
4 uce
For the words: let, letter, letters, lettuce.
I can't speak to whether Postgres uses that index format; I haven't checked. Just saying an index as described above is a textbook idea that's had already been around for a long time when I learned it some 30 years ago.
I also want to share, Date's book is the best book I've ever read on information processing theory. It brought several foundational ideas into my skill set.
