If you needed to look up say the 100 most recent documents, that would require ~100+ disk seeks at random locations just to look up the index due to the random nature of UUIDv4. If they were sequential or even just semi-sequential that would reduce the number of lookups to just a few, and they would be more likely to be cached since most hits would be to more recent rows. Having it roughly ordered by time would also help with e.g. partitioning. With no partitioning, as the table grows, it'll still have to traverse the B-Tree that has lots of entries from 5 years ago. With partitioning by year or year-month it only has to look at a small subset of that, which could fit easily in memory.
Postgres on the other hand doesn’t do clustered indexing on the PK… if I recall correctly.
On the other hand, if you're basically logging to your database so inserts are like 99% of the load, then it's something to consider.