Earlier quoted context omitted.
I understand the feeling for Vietnamese which is a tonal language, and indeed has a ton of "weird" annotations on the basic characters which make the usage of the latin glyphs pointless. But Turkish seems to fit a latin script quite well, and the previous Arabic/Persian wasn't a "native" script for a Turkic language either, I think.
If weird annotations can work for slightly different phonemes in Orthographia Bohemica and for Zamenhof, I'm sure you would be able to use them for tones as well.
A speaker of French, Polish, German, Hungarian or Turkish can muddle through trying to pronounce another European language using the Latin script and get 95% of it but will have no idea of how to read Vietnamese.