It's OK to use that -H digraphs shit in Portuguese or Occitan because H is mute in those languages. However, not in English. Worse: English allows end-syllabe T, P, S... compare THink and caTHouse, SHampoo and grasSHopper, PHylosophy and uPHill.
But it's not the greatest English spelling problem, however... Great Vowel Shi(f)t is worse.
When English spelling was more or less defined, fOOt and fEEt sounded like fOHt and fEHt. WAS and HAS rhymed. bUt sounded like bOOt, and bOOt sounded like bOHt. The vowels shifted a great deal, look at the Wikipedia for more info:
http://en.wikipedia.org/wiki/Great_Vowel_Shift
Is this the biggest problem? No. I can has more.[+]