The practial downside is that, if you get the basic aluminum cantilever with elliptical stylus, record wear will be increased by some small amount as the contact patch of a conical stylus is greater than an elliptical stylus, meaning that for a given tracking force that force is spread over a greater area.
The radical stylus profiles will have an even greater contact patch and thus less record wear, if they are properly aligned, which is not always a given.
The radical stylus profiles will have an even greater contact patch and thus less record wear, if they are properly aligned, which is not always a given.

