I can't think of any reason why you can't have an Aasimar Monk, except for L's decree that there would be no newly submitted Aasimar until March. An Aasimar can be LG, y'know...
And so they're USUALLY clerics or paladins, if they've got a deity. If not, bards. Usually. There are the outliers; that's what adventurers ARE.
Just my three coppers.