The cantrip's description states you can make a sound that can be "your voice or someone else voice."
could a spellcasting Kenku use it to speak regularly without mimickry?
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According to Jeremy Crawford, the Minor Illusion spell can be used to mimic complex sounds like speech,
but you must consider the limitations of this tactic:
The cantrip is a viable way to get around the Kenku's limitations, but it is not without limitations of its own.
EDIT: Although Minor Illusion does not have any verbal components, it's worth noting that Kenku can cast spells with verbal components as well, which could permit communication through more complex spells as well: Source
There isn't much of a difference in the Kenku's restriction on creating new sounds:
However, kenku cannot create new sounds and can communicate only by using sounds they have heard. Most kenku use a combination of overheard phrases and sound effects to convey their ideas and thoughts.
Minor Illusion states:
If you create a sound, its volume can range from a whisper to a scream. It can be your voice, someone else’s voice, a lion’s roar, a beating of drums, or any other sound you choose. The sound continues unabated throughout the duration, or you can make discrete sounds at different times before the spell ends.
This spell is basically mimicking a sound you've heard before (otherwise, you'd have a hard time creating something you've never heard nor seen), so it's effectively replicating the Kenku restriction. In addition, you can't adjust what you're saying mid-cast. It's a preprogrammed sound bite that you'd need to recast each time if you want it to say something different. That would make conversations awfully long.