Unfortunately, UUIDs aren't as universally unique in practice as people think. The standard flavors are banned in quite a few organizations that care a lot about data integrity for valid reasons. Standard UUIDs work for some applications but definitely not all.

For most applications you are better off using a sensible structured key, like incrementing an integer or similar, and encrypting it if you want to obscure it. Encrypting a 128-bit value is approximately free on modern CPUs.