

Even assuming 0 latency on their backend, if you wanted to check each UUIDv4 value again their database during your lifetime, you would need to check 1.686 x 10^27 UUIDv4 per second for 100 years straight. Supercomputers are measured in exaflops, which is 10^18 operations per second, so even distributing the work across many machines, you would need about 1 billion of super computers to be able to have a chance of checking every UUIDv4 value within 100 years.
Not really sure what you mean by reusing UUIDs but theres nothing bad about using UUIDs in URLs for content you don’t want scrapped by bots. Sites like Google Photos are already are using UUIDs in the URL for the photos, and do not require any authentication to see the image as long as you have the URL. You can try this for yourself and copy the URL of an image and open it in a Private Browsing Window. Every so often someone realizes the actual image URL is public and think they’ve found a serious issue, but the reason why it isn’t is because of the massive key space UUID provides and that it would be infeasible to check every possible URL, even if it’s publicly available.