This is a really good question, and unfortunately I don't have a satisfactory answer apart from "that's the way it is." I will see if I can come up with an explanation, though.

The pronunciation reason behind the double letters is something called gemination, where the consonant is effectively pronounced twice. Gemination can't occur with a vowel (like "ah"), so the consonant "h" fills that gap.

A seperate observation is that "ah" can be pronounced ending with a consonant that sounds like the German "ch". When this geminates, the spelling is ah + h rather than ah + ah.