If you want to use UUID for primary keys, the argument should not be the larger key space.

A 64 bit int is enough for a single server. If a 64 bit int PK is exhausted, the data used to store the keys alone would require 128 exabytes, or in perspective, a SAN with 6.4 million 20tb hdds. Then you need several times that to store any kind of meaningful data

If you need to use UUIDs for other reasons such as a high degree of unique keys between servers that do not coordinate, then go for it, but not for the key size.