You're right in that there's a few services that expose this complexity directly, the ones where you're paying for actual storage, but this is just complex, not impossible.
For one thing, storage costs are almost always static for the period, they don't scale to infinite in the same way.
If you did this to a vps the instance might be unavailable until the traffic slows down but up after.
Trust me you would rather they freeze your account.
Is that not a serious request? I play around in the same big-boy cloud as some SaaS company, but I'm on the free tier and I explicitly do not want it to scale up forever, and I explicitly do not want to destroy my credit or even think about having to call Amazon over a $100,000 bill because I set my shit up wrong or whatever. I want it to shut off my EC2 instance once it has used up whatever amount of resources is equal to $X.
Obviously any world with this feature would also feature customizable restrictions, options, decision trees, etc etc. I don't think anyone is or was suggesting that someone's SaaS app just gets turned off without their permission.
If you're worried about getting a big bill, and you don't care if it gets shut off when you're not using it, why don't you shut it down yourself?
AWS made the tradeoff to keep the lights on for customers and if there is a huge bill run up unintentionally and you contact them with it they refund it. I've never experienced them not doing this when I've run up five figure bills because of a misconfiguration I didn't understand. I don't think I've ever even heard of them not refunding someone who asked them for a refund in good faith.
There were no warnings or "don't do it again". They, very reasonably IMO, asked us to essentially explain how and why this happened and how we'd stop it happening again. They then provided some additional guidance and resources around those areas. In the one case where the charges were due to compromised credentials, they asked us to rotate all of our access keys before they issued the refund.
Completely anecdotal and slightly dated information, but that's been my experience.
If you try adding files that will result in a larger bill than your limits over the billing period you warn and refuse.
So simple.