It seems like running it on an A100 in a datacenter would be better, though? Unless you think cloud providers are logging the outputs of programs that their customers run themselves.
Of course they are...
The main reason "the cloud" exists is to log everything about it's users in every capacity possible. That's one reason they "provide it so cheap" (although now they have increased the cost so much it'sfar more expensive than self hosting. So you lose majorly in every way by not self hosting.