Sometimes I wonder if all these people that criticize or that think that a Latin alphabet can be adapted seamlessly to all languages have tried to study past a beginner level any logographic language.
I also think that the Latin alphabet could be easily used for Japanese, which does not contain any sounds that do not have an obvious equivalent in English, and even if it did, we could always repurpose a character or sequence of characters for that sound (do we really need a 'c').
Having said that, the Japanese phonetic system writes voiced sounds as a modification of their unvoiced counterparts. why can't we all do that.
The biggest risk of using Latin is that simply sharing an alphabet could cause spelling conventions of other languages to bleed in.