> ssh -D (socks5 mode) doesn't require root, and can forward both udp and tcp traffic
No, but it requires a SOCKS5 client, of which there aren't many among software I use.
> The trick lies in the "kludgy tunnelling operations" and the "router" (firewall rules)
The other important part of the magic is the packaging. While ssh+socks support is pretty common these days, it is not supported on e.g. dropbear (which is popular on routers).
sshuttle copies whatever it needs to the other side; as a result, there's never an issue of version compatibility (which socks use sidesteps by virtue of using an old, cemented protocol). I have, in fact, needed to modify sshuttle with new options and features for a project, and I was not bound in any way by the existing protocol - whatever changes I made were always supported by the other end of the connection because the connection starts by copying them to the remote.
> I wonder how much effort it would be to get rid of some of the "magic", though.
sshuttle is very well written; It is easy to tear it apart and rebuild it in other ways. But if you took the magic apart, you'd be left with a non-standard UDP-deficient SOCKS-alike system. Why would you want that?