Not really. I'm not implying jack or shit. I am claiming that your idea is OP, and not at all balanced.
What's wrong with a tanky tryn getting soo much free tenacity and MS? Did you suddenly forget what his ult does? Now imagine that on a bruiser that is damage oriented with a pretty good dash and a heal. Pretty much what he becomes. IMO becoming actually unstoppable and immortal during the duration of the ult being allowed to kill anyone who doesn't have kassadin level mobility is a little BS.
Yi while different, still becomes a damage oriented bruiser when built tanky. Now imagine that his ult makes him twice as fast and almost immune to CC. He becomes a quasi-old olaf. Not good for the game, not even close.
The counter to Mundo is kiting. His cleaver and meatiness is all he needs to get over that hump. Mundo beleive it or not, only has 1 thing keeping him from being over the top, and that is greivious wounds. The same reason why most Heal over time champions are weaker. Even Morello admitted that the mere existance of grevious wounds in the game as prevelent as it is keeps these selfish healers down. He also admitted it made them very difficult to make good. Mobility creep is actually something that Mundo doesn't feel like most other melees, due to being able to consistantly dps and keep up with Q and R alone.
And Chogath would be over the top. Most people agree he is balanced right now, and as a result is not played so much. Giving Cho gath effectively free MS and Tenacity simply for being Chogath is OP, as you are buffing champions that simply don't need it. Gimmicky meatwall? Sure, he is meaty, but he can do incredible damage and CC. He is balanced around being immobile, as if you add mobility to him he gets really crazy, really fast.
This, of course, isn't really considering those champions that are only managable due to NOT have mobility. Consider Garen. Late game, kiting is truly the only way to really handle him, as he is rather meaty, heals like a sudo-mundo, and does a pretty good amount of damage if he can get in range.
In the end, yeah, it really is an issue to make a class defined by their weakness and lack of mobility immune to their main form of counterplay. I remember Season 2. Apparantly, you don't.