I used Mailinator as the quick solution to access some one time resources on websites that forced me to register. It was the simplicity of the throwaway email that made it attractive to me. But when it's blocked on a website I usually wouldn't want to bother with c more complicated setup. If the effort is justified then I can probably use a regular email address. Other people might have different use cases.
I'm not sure if my use case was clear or perhaps I don't understand what the scenario you present does.
Say I want to comment on a news article and need to register. I don't want random-newspaper.com to have anything directly related to my person, including anything @mydomain.com. So I quickly punch in random-email@mailinator.com to register and once I'm done I can either forget the site and email ever existed or keep using it since it's non critical and losing access to it doesn't matter.
Ideally I would have different email addresses for every site so I can keep those identities separated and free of any personal information. Last time I used it like this was probably a decade ago because since then more and more sites starting rejecting @mailinator.com addresses. I found another such solution that I have been using for the past years but this is also going the same way (not a big issue yet).