No, they wouldn't. It's not good design to have a champion with that crippling a drawback. The self-cripples that are already in the game stem from champions that cast from HP, Sion's ult when he hits something, suppressions, the latter half of Blitz's speed boost, Vi's chargeup on her Q, Xerath's chargeup on his Q, Tahm Kench after eating an enemy champion, Soraka's heal, and Rumble's passive, and are more or less a slightly weakened state as a response to using a skill, not from just existing. In fact, all skills that revolve around the current state of your HP incentivize you to keep your HP as low as possible to benefit more from it, despite the greater risk.
Doing it the other way around would create a champion that becomes considerably less effective the more he gets damaged, which means the lane opponent will harrass him more and the jungler will gank him more, all for the wrong reasons. While this can be negated later on with Warmog's and other such healing skills and items, this doesn't mean anything for the first 1-2/3rd of the game, and that's only if he rushes them from the very start, and he shouldn't need to do that just to claim a bigger stat dick. Even then, when it came to mid to late game, their menace is diminished considerably the instant a teamfight starts, since the enemy has to focus him just long enough to bring him down to half, and then focus everyone else while they are down a full champion (half if he doesn't recall or back out of the fight).
In short, no. It creates a technical and balancing nightmare to handle for very little benefit other than having a larger stat dick.