And using their servers and resources without generating them any revenue is not abuse? They clearly don’t want you to run a third party app without ads, yet you feel entitled to it?
No, it's not. In this case, abuse is about intent: DOS intends to cause distress, losses and denial of service to others. Use with third party apps without adds intends none of this: the intent is to use something else to access the service in an otherwise normal (to the user) way.
Arguably third-party apps that are scrapers are somewhere in between these two in acceptability, but that's a question of "are scrapers morally fine and should they be legally allowed", not a question of whether third party clients are to be allowed at all.
If I access your API I’m using your server because you offer it publicly. That is not abuse.
The distinction is about whether you should be able to offer something publicly, taking advantage of public infrastructure to do so, and then make demands about what the public do with that.
Companies want to do the electronic equivalent of putting copyrighted media on a billboard in a public square then claiming you need to sign a contract to look at it and then only through special glasses they provide.
