The bigger the scarier! I've never thought about increasing the MM giants' size, but why not trying that sometimes? There are of course Huge and Gargantuan giants already, but there's really little reason why Frost & Fire should be smaller than Storm & Cloud an not viceversa.
There are however some difficulties in using too-large monsters, because you have to accomodate their environment, at least if you want it to make most sense as possible.
Indeed I agree that the best would have been to have advancement by HD/size. IMO when writing the MM the designers had in mind that each monster should be suggested for either advancement (HD or class level) but not both. So they might have automatically thought that if they had written a HD advancement it would have meant "you shouldn't apply class levels to this". Class levels is still the most appropriate advancement for Giants, but really they could be advanced in both ways.