In my experience with combat taking a long time, it's rarely been because of those numbers (although that 16 str halfling battlerager with an axe before Expertise was a thing did start to really suffer as we started to approach paragon tier) and almost entirely because people take forever to execute their turns. For some of those players, I feel like your houserule would actually slow down combat even more, as their options multiply. I can see it working well if your table is more easy-going with their choices, though.

It will shift the relative values of various options, both build-wise and tactical, though. Things that extend your HP supply (regen, temp HP, etc.) becomes more valuable because it's also an offensive resource, to-hit and damage bonuses become less necessary since you can make up for it. Thinking about it like that, I kinda like it, honestly. I think it's more interesting as a 1/round thing or so, though, because that closes the gap a little between multiattackers and non-multiattackers. Of course, if the goal is just to speed up combat as much as possible, you just want a bunch of rangers and a lot of surgeless healing...