I agree that dwarfs get more than enough bonuses to be worthwhile without increasing their to-hit chance. Higher hit dice, Fighter combat options (not a minor thing, with ACs topping out around 21), better saving throws, and an increased Constitution Modifier.
Now my version of LotFP has a handful of houserules, the first being that a character's Attack Bonus also applies to damage rolls (to stop Magic Missile becoming the only way of dealing meaningful damage to high HD monsters), so I'd be more than happy to give dwarfs, halflings, and specialists increases in their Attack Bonus at every third level up to +5 (which would be at 13th level), but it's not something they actually need. Although note I've also modified the Saving Throw rules to use d6s and standardise across classes, which results in high saves not being a bonus for a class.
But without ACs in the mid-twenties a mid level dwarf is par with a mid level fighter, although magic-users still end up being the best of the whole set (an unfortunate side effect of high level magic being that powerful and the standard casting system having resource management as the only downside). The Fighter doesn't actually catch up in the higher levels either, due to their Saving Throws capping at about three points higher than the Dwarf.
Will most parties prefer a Fighter to a Dwarf? Probably, that to-hit bonus is a massive boost, but having a stout dwarf who just will not die is just as good if not better in most situations.
The Dwarf is the LotFP class I want to play the most for that reason. No fancy spells or scaling attack bonus, just a beard and a the inability to die.