SMTP might be a better analogy, but I'll concede as it's irrelevant.
You're wrong about the compensation bit. It's entirely possible to send fake traffic and get compensation. Cutting that off is an entirely manual process; with someone noticing the fraud and reporting it. It's not some magic authentication that happens.
The reason things like sex lines (either premium rate numbers or just really high-rate areas) often do not work is because the costs are passed on through the various companies (so they'll clip anything over a few cents) or because they simply will not accept calls if they are not within the trusted system. If you have a VoIP line and try dialing a 1900 number, it won't work unless that VoIP provider has made a specific deal. It's not like they look at the calling number, then mail out bills to whoever they think the owner is.
Guess what: Folks don't accept limitations on dialing 911 (or the PSAP admin line, which is just a normal number). They're going to demand 911 be answered regardless of billing relationships.
At both 911 companies I've owned, the routing system depended on being able to "spoof" caller ID. We would have to accept whatever caller ID we were given, because there's it's essentially intractable to know who has the actual relationship with the end user. It's also not knowable if the connection handing me off this call is authorized to use that number. There's simply zero concept of that. Additionally, there's no such thing as a real master database correlating number-address. (That'd make things easy easier!)
Even if there was, it'd still be trivial to swat. Buy a number online, say your address is <target address>. Place a legitimate call that "authenticates". Change address, repeat. Worst case scenario (if you can't make an anonymous payment), hack someone else's VoIP account and change their address and place call.
You are right that this is a large problem. Some PSAPs have come under DoS attacks, getting a flood of fake calls. 9-1-1 is a critical piece of safety, and it's fairly unprotected. Funding is limited. Some of the vendors involved are laughably bad. And, at least a few years ago, there was a massive disconnect between technology/Internet and the emergency response side.