Since the transmission is not just for driving the bike, but is also the connection between the charging generator and the engine, it’s automatic control is necessary as part of managing the battery level.
Now if you had an old fashioned simple EV system like the first Honda Insight, where the electric motor and gas engine are directly connected and can’t spin independently, in that case you can have a regular manual transmission, as those vehicles did. However, they are much less efficient and versatile, and don’t have a useful EV only mode.