I also strongly disagree. The real problem is that browsers can't use them as good as they should.
If you take for example a RESTful API, the verbs make totally sense and especially one of the mentioned verbs. PATCH is a great verbs if you use it like it was specified.
I personally like the idea of giving more freedom to chose the verbs.
Imagine you could use for a Twitter API something like:
FOLLOW /users/123
The HTTP specification in no way restricts the verbs that you can use to those that are in common use. But at some point somebody, somewhere, decided that the only ones allowed were the ones that the specification explicitly mentioned. And so people just shoehorn their applications into frameworks built around what the HTTP specification defines, rather than allows.