Problem with sprinting characters is they would be highly ineffective early/mid game while all the towers are still up, since you would have to pursue past a heap of towers alone to get the kill.
Slows prevent the opponent from retreating effectively and promote better use of combat potions/teleport scrolls.
That said, Unclean Beast is a fast mover, Vamp. Lord has the blink type ability (Bat Swarm?) and Warpstones are available for anyone who wants them.
As for invis, that would mean giving towers true sight (if they dont already have it) making it largely ineffective as most fights take place near towers for the majority of the game, although I do believe there should be more in the way of invisible things, since as far as I know Regulus' mines are the only ones, maybe a general item that cloaks their nearby minions, like Arbiters in Starcraft, to make enemies think they are alone or something would be cool.
