There is even services that scan the whole ipv4 in less than 5 minutes: https://zmap.io/
And a list of how to do it: http://www.securitynewspaper.com/2015/10/15/how-to-scan-whol...
https://nakedsecurity.sophos.com/2013/01/29/what-if-your-sec...
https://en.wikipedia.org/wiki/Universal_Plug_and_Play#Proble...
I'm somewhat curious if all those attempts count against my data cap.
I don't see why they wouldn't. IP (which is really the layer ISPs should operate at) does not distinguish between packets that you have "requested" and unsolicited packets, being connectionless protocol and all.
There is nothing inherently wrong with port scanning and it should not, by default, be considered "abuse".