In many ways, it's beautiful in that it allows Autonomous Systems to come together and independently make the Internet.
However, I always felt it was brittle in that it relied every AS to have edge routers aware of the entire AS routing map, and so when those routers went down hard, when they came back up they were blank and needed to learn the Internet again. I noted back then that on some routers a single spoofed UDP packet to a router getting a table from its peers could cause it to stop doing that and start again. In a time when those updates could take hours... well... that kept me awake at night sometimes.
Propagation of routes was global and error prone. Even today, you can see on the spy glass websites rogue AS routers advertising crazy routes either by accident or on purpose as a hostile act (to try and get traffic for a target network through itself).
There are tens of thousands of engineers globally nursing and managing this stuff to keep the whole thing going.
Like I said, it's been a while since I last looked closely, and I imagine multiple improvements have been made in this space since that time, but if there was ever a protocol that needs a long, cold hard look for a replacement, it's quite possibly BGP.
It's also the one - and only - non-crypto situation where if somebody asked me if a blockchain could be really very useful, I'd say "probably, yeah".