As a MUD enthusiast for 37 years, I learned to program in C and Unix through TinyMUD, MUCK, and MUSH derived servers. From the beginning, none of these codebases implemted Telnet. There was nothing but a raw transparent TCP connection. In fact, I facilitated the introduction of a grand innovation: the "port concentrator" system which multiplexed TCP connections. Unix processes had a hard rlimit of 64 file descriptors, which crimped our style as an emerging MMORPG. The multiplexer increased this to 4096, for the biggest games of the era.
You mention MUSHclient, and I do not know about later revisions of the TinyMUSH server, but I can assure you that every MUSH I found from Larry Foard on, was not implementing Telnet. (I was privileged to help Larry "test" new features as I red-teamed his server with bizarre edge cases!)
Likewise, after I handed off TinyMUCK 2.3 to the furries, it was not doing the Telnet protocol. When we backported stuff to MUCK 1.x, it was not doing Telnet. I wrote a bonkers Perl program to read MUCK databases and sort of implement the game. No Telnet there. I've got to wonder whether the Ubermud or MOO guys had folded it in; they were close collaborators with us, back in the day.
Now as for the Diku, LP, and other “combat” type games, I’ve no idea. Perhaps they did. We never cared. I was aware that some of them had a pesky “prompt” that violated the line-mode assumptions of conventional clients and needed workarounds.
telnet(1), the program, was historically the only program that implemented the protocol. If you use Tinyfugue or Tinywar or tinymud.el, they are not, and no, I am not confused, because I was giving an example of why the Telnet-implementation, the program, the client, was so inadequate for playing on MUD servers.
It wouldn’t have been difficult to retrofit the Telnet RFC 854 into any MUD server, but none of us wizards had any use for it, seeing that our clients were mature and capable of much more processing without it.
If modern MUD servers have mostly implemented Telnet, then that is cool, but what surprises me is that it is mandatory, and your clients don’t seem to interoperate without it? That is a strange reversal!