I'm specifically wondering about Irish deriving from Ogham, yet when written in the Roman alphabet, there are tons of unique pronunciation rules. Why would people (who already have a written language) adopt the Latin alphabet and not inherit all the pronunciation rules?
The Latin alphabet was invented for recording of the Latin language.
Other languages often use phonemes not present in Latin and they need to represent them somehow. They can use clusters of traditional latin letters or they can invent new letters by adding diacritics.
Some languages did both in their history. Here is an example of the ancient Czech orthography:
Iat byl prsieliutym pohanem
Cziezzarsem domicianem
Tet gho chtye muchzity wzzady
W oley wruczi w pylney cady
As you can see, there are lots of digraphs that represent the extra phonemes.
Later the Czech orthography was reformed to use diacritics instead and today the same text would look like this:
Jat byl přělútým pohanem
ciesařem Domiciánem.
Tet jho chtě mučiti, vsadi
v olej vrúcí v pilnéj kádi.
The problem can get even more complicated when phonetic changes take place - the orthography stays the same but the pronunciation changes a lot. That's what happened to English (besides other things like the influence of French).
What used to be few simple rules evolves into a complex of complicated and often redudant rules that seems to be illogical.
This question is probably better suited for /r/linguistics' Q&A Thread.