I don't know why Aramaic and Arabic write them with different letters, possibly because of pronunciation differences. The way people speak used to change markedly from place to place before radio and TV came to homogenize the language.But if they were really the same root, then why Aramaic write them with different letters, and so Arabic does.
shouldn't we expect it to be the same in every language?
It is very fine to "expand our view" and get out of the "closed bubble", in considering also Aramaic and Arabic, except that the genetic relationship between Hebrew and Arabic is unknown. Entering into the enterprise of comparing Hebrew to Arabic to Aramaic, would require of me making a vast number of assumptions and speculations, as is far beyond my intellectual capacity.If you want to look at the Hebrew language as if it evolved inside of a closed bubble, then it is your choice.
But I guess you would accept the fact that Hebrew is part of the Semitic family, and so while examining Hebrew (or any other
language) a lot of times, we need to expand our view and look at the behavior of the family.
Having said all this, I have to admit that you are right even far beyond what you so vaguely claim. Hebrew has right now 5 (five!) different xet letters. They are
ג, ה, ח, כ, ק
The letter ה is the letter ח with a disconnected left hand leg. The letter ג is the letter ה with a leaning left hand leg. The letter כ is the letter ח resting on its side, and the letter ק is, again, the letter ה with a slightly elongated left hand leg.
How are the words
חָם, 'father in law'
חוֹם, 'heat'
חוֹמָה, 'wall'
חֶמְאָה, 'butter'
all from the same root קם= גם = חם interrelated? By the realization that חוֹמָה is really a קוֹמָה, 'a lofty wall', that חוֹם is really a קוֹם, 'high temperature', that חָם, is 'an adult', and that חֶמְאָה is as solid as a חוֹמָה.
Isaac Fried, Boston University