As long as such abuse doesn't cause monetary or resource exhaustion concerns, it's quite OK to ignore it, but stories like "whelp, turns out that 80% of the capacity of our auto-scaling fleet is not doing anything useful" are depressingly common enough to at least keep an eye on things.
My annoyance with this kind of abuse revolves mostly around logging: a majority of logs just showing the same set of hosts displaying the same pointless behavior over and over again. Again, not a huge issue if your log storage is cheap and plentiful (as it should be), but having some kind of way to automatically classify certain traffic as abusive and suppress routine handling of that is definitely a good idea.
It's also a lot harder than it sounds! I can't count the number of times I've added classification logic to my inbound SMTP server that should pick up on outright, silly abuse (of which there is a lot when dealing with email), only to have it triggered by some borderline-valid scenario as well.
Spending way too much time on going down successive rabbit holes is a great way not to get any real work done -- a great reason to outsource, or, if that's too much work as well or just too expensive, indeed just ignore the abuse, annoying though it is...