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.
Nitpick: It's actually 7.38 million disks since "20 TB" for a disk means terabyte, not tebibyte.
"This function generates a version 1 UUID. This involves the MAC address of the computer and a time stamp. Note that UUIDs of this kind reveal the identity of the computer that created the identifier and the time at which it did so, which might make it unsuitable for certain security-sensitive applications."
I guess that's not immune to problems either (i can imagine problems with both mac address and time).
What would the B+Tree look like for over 2 billions UUIDS where there is no order within? Also, the cache locality problem.