One big advantage of phonemic scripts (alphabet, abjad, syllabary, abugida) over semantic ones (logography, idiography) is that they’re simpler, smaller, and easier to learn. Languages have fewer sounds than concepts they can express with those sounds. But at what point would a language have so many different sounds that having a semantic script would be simpler than a phonemic one? Is this at all realistic?
This is more hypothetical than a lot of stuff to do with conlangs. It seems to me that this would only be the case in a language with thousands of distinct phonemes. Wikipedia’s list of languages by number of phonemes doesn’t mention anything close to 200. Even with lots of digraphs any phonemic system for a remotely naturalistic language should be simpler than a logography.
It depends a lot because “simple” and “complex” can be a thousand things. For example, a purely semantic system would be easier to adapt to unrelated languages with wildly different phonologies - because it doesn’t refer to the phonology at all.
But if by simple/complex you’re talking about the number of basic symbols, I guess ~5k phonemes would make the alphabet as complex as a logographic system. But by then perhaps the best solution is neither, it’s a featural writing system.