A hyper elliptical must cause more groove damage than a conical as the contact 'patch' is less and the forces greater on the groove walls for the same tracking force.
Actually it is a question of total surface area, and it varies depending on the specific shape and the resulting total surface area...
A spherical 0.7mil (18um) has contact surface area of approximately 320um2
A Large Shibata = 6um x 75um has contact surface area of around 450um2 (so total surface area is larger!)
A small shibata = 6um x 50um has contact surface area of approximately = 300um2
The very narrowest of line contact types may well result in increased wear, as their contact surface area is actually smaller... eg:
MicroLine = 2.5um x 75um = 188um2
But the vast majority of line contact designs are within 10% of the total surface area of a 0.7mil spherical (varying from 280 to 450um2)
The large shibata design is one of the best in terms of wear due to it not going to extremes with regards to contact patch narrowness (it is small enough to track up to 40kHz... which is what it was designed to do!) - while maintaining a nice long vertical contact length - resulting in the largest total surface area of the geometries for which I have specs...
The other sides of the wear equation are 1) VTF - high compliance designs with low VTF cause less wear (dramatically so) and 2) proper tracking, absence of mistracking - as mistracking will dramatically increase wear.
Our current mass market penchant for mid to high VTF (low to mid compliance) cartridges is not good for vinyl wear over the long term.
And yes it bears repeating, that sacrificing proper tracking for low VTF takes you backwards, as mistracking is far worse than high VTF... but a properly set up high compliance cartridge in a low mass fluid damped (or equivalent) arm is the best option for reduced wear.