You don't have to immediately delete customer data.

Most service that has a limit cap will have a "grace period" of a couple of days during which the service does not work but the data is not deleted. That give your some time to get notified of the issue, and fix the problem/increase the limit.

This is a solved problem for every other service out there. You don't just delete the data, you give the customer a few days, weeks, or a month to pay their bill and if they don't, then you delete their data.

The problem with this though is it opens a vector for exploitation: users could just use the grace period to store data for free for a period of time. This can quickly become a heavy financial burden if enough people do it.

You could factor that into the price, but then you're potentially making the price point even more unattractive to users than it already is, and users that are responsible with their budgets would be subsidizing those that aren't. Not a very workable solution.

I'd say a good solution is giving customers the option to stop accruing more storage capacity, and to have a max deadline accounted for in their budget to store data (basically each customer decides whether or not to pay for a grace period).

I've accidentally let my OVH subscription go unpaid, and they gave a 7 day window to pay my invoice or delete my data. That's seems pretty fair to me, and they seem to have wide enough margins to eat the cost and still offer some of the cheapest prices out there right now.