I assume people in the banking industry allow them to operate as a way to hold leverage over the crypto markets and absorb capital that would otherwise flow to altcoins.
It really isn't counterfeiting. If you made fake hundred dollar bills and passed them off, that'll be counterfeiting. However, if you decided to give a bunch of people $100 IOUs and claim they're "totally backed by real dollars in a vault somewhere", but they're not, then it's just fraud. The NY AG and/or CFPB were able to prosecute/fine them for that, but they also got rid of the "totally backed by real dollars in a vault somewhere" claim, so whether they're currently committing fraud is unclear.
Tether is just an IOU note. I don't have problems with IOU notes, unless someone forces me to use them. Personally I haven't used tether and probably never will, however I don't have any problem if someone else wants to use it.