Well let's test it out. How many genders are there (Wikipedia lists over 50), and what defines what constitutes a gender? I'm especially interested in the ones that aren't man or woman - how are they defined?
Asking "how many" isn't asking "what". Gender is a societally constructed performance. The requirments of that performance are maleable and inconsistent across time and geography. There's not really a limit on how many their are or could be.
Sounds like you're just describing "personality" then. If you can't define what constitutes a gender, then there is no such thing as a gender and therefore no need to transition between them.
You've done a stellar job proving my original point. But yes, a genderless society would be a more just one. If your perceived gender didn't affect one's life outcomes there would be little reason to perform them.