I proxy only 802.1x traffic to and from from the AT&T modem and spoof my external MAC as the AT&T MAC. The AT&T router is not in the data path nor can it make any other connection beyond the 802.1x traffic (I have no IP on it's port to act as a gateway). Been working fine for over a year, performance is far better than when the data was running through their router even after disabling everything I could find.
Also there is a lot of hidden config on that router, for instance when Cloudflare announced 1.1.1.1 it wasn't reachable from my AT&T connection. Coincidentally that was the same week I swapped to my own router and when I did instantly 1.1.1.1 worked. Swapped back it didn't. So somewhere in there there were IPs and config that weren't showing in the user interface. They fixed the 1.1.1.1 issue in their routers about a month later.
There's no rental fee, but if it fails, you'll have to deal with the ISP to repair your service.
That being said while on the topic yes you usually need a particular ONT for compatibility but there is no reason it would need to be a perpetual rent model or have the ISP logo on it. As for multiple connections being on a single shared line sure, that's how cable modems have operated for years without issue with consumer choice.
AT&T's network uses 802.1x authentication and the client certs are burned into ROM on the router.
The router has a crappy passthru mode where it gives your own device the external IP and sends any traffic to it, but under the hood it maintains its own (rather small capacity) NAT table for all the traffic. There's not a real bridge mode.
Some more technically inclined folks have come up with solutions like a proxy that just forwards 802.1x traffic to the router so it can respond, or rooting the AT&T box and pulling the certs out of ROM so you can use them to auth on your own network device.