I understand the numbers and they are real, but something that should be pointed out in MattY's example is that his theoretical couple would likely be better off cohabiting while unmarried. Two impoverished cohabiting "single" parents would likely qualify for more benefits and breaks than one not-impoverished married couple with two children.
It's not universal, but the way that we treat income with respect to marriage means that it is often better financially for dual income households to not marry than it is to marry (there are other benefits to marriage, mind you). I think the simplest solution is to drop the entire section of the tax code. Everyone who files is the same (so no single/married/married filing jointly/head of household crap). Pick numbers in the middle and leave it at that.
Now that does seem to penalize single income families, but in reality it doesn't: you can have the traditionally working spouse pay the not-traditionally-working spouse half the income, and so split the pie lowering taxes all around...yes, I know that can be complicated, but since my fantasy tax filing would also drop lots of other crap, this would actually be pretty easy.