This is also why you do not let your web designer own and operate your website hosting.
No, this is why you pay your web designer for their work.
If they haven't paid you and you happen to own and operate it, just turn it off completely, there is no professional middle ground.
If a mechanic fixes your car and you don't pay them, in many places have have the right to seize your car until you pay. But they do not have the right to tamper with your brakes or spray paint "pay me" on your windshield.
The problem here is the dispute that's occurring is being settled through taking the client's website hostage. That's ridiculously unprofessional.
1 - Cloud services are for experts. It's too hard to use one and not have it backfire, lay-people have no chance here - most of the times, it will backfire and you won't even know it.
2 - Don't stiff the people whom your survival depends.
Now, of course, #2 is only an issue for people that stiff people. And for those, good luck trying to determine who should fit under this rule.