I don't see that as a valid security concern in this case. Yes, it will break your code or do unintended things. In order for this to happen an attacker must have access to the page in your user's security context, which means some other preventable security violation has already transpired. This applies equally with any application/language. Even if you could freeze the DOM such that nothing can be assigned to object properties then you might be able to ward off DOM clobbering, but there is still a malicious user in your security context reading all your secure and private details. If you prevent the malicious agent from access this security concern with the DOM is eliminated.
In other words whether or not DOM clobbering occurs a prerequisite security violation is necessary and hardening the DOM won't provide the necessary solution.
Aside from malicious third parties intentionally writing over event handler assignments DOM clobbering really comes down to poor code management, which is the real security problem here. That makes this a stylistic concern. Additional layers of concerns isn't going to make people instantly less lazy. There are better ways to solve for this.
> HTML elements implemented in completely different ways
HTML is not the DOM. These are separate and unrelated technologies that are maintained in very different specifications. This separation is not an accident. It is by design. I know this is a contentious point, about HTML and the DOM being far separated.