Do phonetic writing systems reduce the occurrence of free variation in a language?

Just to make sure we are on the same page

When I say "phonetic writing sytem" I mean a writing system in which a sequence of letters maps to exactly one pronounciation.

and when I say "free variation" I mean the phenomena where a word is pronounced differently by different individuals outside of dialectical variations. Examples in English are words like "pecan", "caramel", and "gif".

Basically, my hypothesis is that if the writing system only offers one way to pronounce a word, and everyone knows the rules of the writing system, then there can be no debate on how to correctly pronounce a word (outside of the consistent dialectical variations). So I do not expect for Spanish as an example to have words analagous to "caramel" outside of relatively new loan words