If the system has a problem during the night, the users will wait until the morning.

The world doesn't stop because a streaming service is down for a few hours. It's not a medical service, or something thousands of businesses rely on.

It just looses a bit of money and users are grumpy for a day because they had to wait until they could access new content.

It's ok.

The company I work for has a lot of stuff in the cloud. We seem to have quite a few position's worth of people permanently on call.

The percentage of "data center"-type on-call situations has perhaps gone down somewhat since moving into the cloud, but it has not gone to zero, and it was never the majority of problems anyhow.

It seems like you're sneaking the idea in that if they would just pay a lot more money, the person on call wouldn't have to be on call. I'd like to know what cloud you're using, because it doesn't seem to be any of the ones I know of. If your service is critical to your business or project, you've got someone on some sort of call (maybe not overnight call, which is the really rough bit), period, or you've got a business that can disappear at any second.

Like.. what are you expecting to happen? You'll just gaslight them into thinking they dont know how their business works?