uTP (micro transport protocol) is a TCP implementation based on UDP. Used by the majority of BitTorrent clients. It seems to work pretty well.
It's interesting that you think TCP was a bad idea. Do you have any sources or reading material that you can share?
TCP is ok, but it has a lot of flaws with handshaking and long lag, and also is useless for things like gaming because it can't go through NAT (NAT itself is a disaster too). TCP has created an internet of second class citizens who can only download but can't upload. The worst thing is, IPv6 will repeat all the same mistakes, so I think of it as second class citizen 2.0.
If it were up to me, I would scrap the whole thing, especially the needlessly large UDP and TCP headers, and make a simpler scheme that only contains the destination IP address and maybe a small key that references metadata held in each endpoint's internal state. So the TCP protocol would only exist in each endpoint's TCP stack, not on the wire.
I don't really have any sources, but I lost two years of my life trying to write a windowed reliable transmission scheme over UDP that can punch through firewalls, basically what WebRTC is trying to do, and got thoroughly disillusioned with networking. It just never, ever, ever works 100% reliably, so you end up recreating the work that Skype did if you want a connection as reliable as TCP. I think that says a lot about the miserable state of networking today. I might get down voted for this, but I feel that what I've said is a statement of fact if you look at the hoops that P2P protocols have to go through today. That mess was never the intention of the original network architects (except for admins maintaining corporate firewalls who want their users to be second class citizens, who sadly had a hand in the NAT used in home broadband modems).