I would say when you have something that is going to be cheaper for you to have it in your own server. Not all servers are that expensive (you can even use an old PC for this purpose)if they is only going to be used for a limit amount of users.

Specially when you are going to do a lot of dev/tests in your Cloud server, that for sure can raise the costs way more than expected. I know teams should first test on their local machines and then push everything to the cloud server, lambda, whatever you use... but, devs usually don't respect this...

And yes, for many companies their data is still a really valuable asset that they don't want to share with anyone.

When you are the cloud vendor.

• you're running a web crawler and many sites filter cloud IPs
• you have high CPU or GPU demands, you will be paying ~3x in the cloud
• you are doing something against the cloud vendor's TOS (e.g. bitcoin mining, network scanning)
• You have existing PCI- or HIPAA-compliant infra (only a subset of AWS services are HIPAA)
• you need to provide a private messaging service like Proton or Signal -- these need to be run e.g. in switzerland or panama

here's another good example. basically any MTA / SMTP stuff on EC2 is a pita

simplelogin.io/blog/we-left-aws/

When you need extreme low-latency to another system (for example, algorithmic arbitrage trading systems need low-latency connections to stock market systems)

Good discussion on HackerNews-- one example shared a cloud quote that was > 10x more than traditional hosting.

news.ycombinator.com/item?id=23089999