Just for fun I thought I would try my 4770K in the GA-H81M-DS2V. While extremely limited because of the 1.2V ceiling, the "K" CPU is indeed overclockable on this budget board, at least to a rather lackluster 3.99GHz:
Maybe the ability to adjust multipliers is an all or nothing deal, and the way to keep savvy users from using low-end boards is to limit the voltage.
Of course, with only 2+1 power phases, it's likely this board couldn't take much more anyway, which is another good reason to limit voltage!