When the original hyperelliptical was introduced, the advantages according to Shure (who designed it as their answer to JVC’s patented Shibata tip, to avoid paying a licence fee to JVC to use the Shibata) included the fact that as an extended line contact it provided much lower distortion (both THD and IMD) than the other stylus shapes they sold.
Shure introduced it on their 1978 best cartridge, the V15 Type IV, and their figures showed that second harmonic distortion percentages at 8 kHz for the different stylus shapes were:
Spherical stylus 6.4%, hyperbolic 4.0%, elliptical 4.0% and hyperelliptical 2.8%.
Intermodulation distortion percentages for the two frequencies 1 kHz and 1.5 kHz for the different stylus shapes were:
Spherical stylus 2.8%, hyperbolic 1.8%, elliptical 1.8% and hyperelliptical 1.4%.
So those are fairly significant reductions in distortion, and should be worthwhile, particularly as you’ll also be getting less stylus and record wear for a hyperelliptical compared to an elliptical. Whether an aftermarket hyperelliptical is as good as Shure’s original probably depends on the maker, but if it’s a reasonable copy, the same advantages should be available.
So if advanced stylus profiles are so beneficial to have, what is the reasoning behind quite pricey cartridges still sticking with spherical / conical tips? I can understand why a cheap entry level cart would have this due to manufacturing costs but why would, for instance, AT5e @$95 or Denon DL103 @ $200 feature a conical tip?
Are there some cases where a conical tip is actually preferred?
The AT95E actually has an elliptical stylus - that's what the 'E' in AT95E signifies - it's a 0.4 x 0.7 mil elliptical. But if it was available with a conical (it may be - perhaps there is an AT95C!) it would cost a bit less.
The Denon DL-103 has been around for 50 years now (introduced 1963), and is a nice sounding cartridge, which is why it's stuck with the conical stylus. But they have produced modified versions with lower tracking force and elliptical styli, such as the DL-103S, DL-103D and DL-103M, which were all pricier, but sounded better, with better high frequency response. It's just that because the DL-103 is relatively good value, since the original design costs were paid for long ago, that they've stuck to that design for over 50 years - they have also modified it in various ways, including with elliptical styli.
The main reason why a conical stylus is preferred is usually because it costs less - the more complex shapes all take longer to make, and cost more as a result. A conical is also much easier to set up - other shapes require more careful alignment, or distortion is increased, and the full potential of the better shapes won't be reached.