Yes, with this solution, internally it could be seen a two separate torrents, but if it is an option easily accessible in the client settings, and it is handled transparently as a single torrent, much more people will do it, and the scene as whole would gain with the network effect.
Your suggestion would purposely share the same exact private torrent infohash into public DHT/PEX,
Yes, but not necessarily. It is trivial to recompute the infohash with the private bit disabled. This would split the network, but that is probably a good thing to preserve the anonymity of the private tracker users, as pointed out by another commenter.
I don’t see how.