That has to do with the definition of what a word even is (an open problem!). "Alot" is clearly made up of two separate units, but so is "anyway". I think a lot of people don't like this one because it's simply unnecessary. You need "anyway" to show that the two words are not stressed separately, but treated as one unit, whereas with "a lot" this is already obvious ("a" is almost never stressed).
Also has to do with English spelling just being bad, generally.