That's not a problem. I don't mean that in the sense that it doesn't happen. Rather that the market succeeds despite it. People forget to pay fines, mortgages, taxes -- the system has rails to put most back on the correct path. And the failure isn't permadeath. Your domain expires and life goes on.
There are also protective mechanisms to prevent your domain from expiring. You can pay a balance in advance. Pay for "renewal insurance", etc. As more people use the system, it will grow even more safety rails.
Replace 'domain' with 'identity' and you have a very scary proposition. This is just another form of 'code is law' and doomed for all the same reasons. Bugs and exploits become severe threats to your wealth and well being. As much as we hate to depend on institutions and 'other people', depending on computers program is inherently worse.
If you use your domain for email, you already have this problem.
This problem isn't new at all.
Would you rather have a situation of ownership with responsibility or no ownership at all?
The "free" alternative is a crypto like identity, and there's zero restitution if you lose your key. People will struggle even more with this. At least with domains there is a legal framework if you're paid up.
There are also protective mechanisms to prevent your domain from expiring. You can pay a balance in advance. Pay for "renewal insurance", etc. As more people use the system, it will grow even more safety rails.