Saeviomagy
Adventurer
Rogues with strength as a secondary stat will be perfectly fine at grabbing, and in fact get two powers that make use of grabs.The fancy-schmancy attempts at proving it mathematically broken seem to fall apart once you look up actual monsters you'd want to grab (skirmishers and lurkers, mostly). But the fact that your typical character is carrying something important in both hands is an awfully big deal. Fighters, Paladins, strength based Clerics, Rangers, and Warlords- they're all likely to have both hands full. The only classes that might not are Rogues and the various arcane spellcasters, none of which are well suited for grabbing.
As for your 'versatile fighter' idea - I think that introducing a "your empty hands count as a melee weapon of your choice that you are proficient in" feat would go a long way to making a large number of currently difficult builds very easy to do.
Beyond that, more powers similar to the rogues grab powers (garrotte and stab 'n' grab) would seem to be all that's required, rather than an entire new class.
Incidentally I find it interesting that one of the best ways to improve your grabbing capabilities is to improve your fort defense.