Is my brain failing or did someone make spherical centers that contacted the 60* drilled parts more in a circle than a cone ? It was supposed to let shafts be less affected by misalignments than normal centers ?
"Ball end" tips are still common in sets of live-centres with swappable tips.
Their PRIMARY use is to manage offsets for turning tapers, 'coz the reduction of contact area to a narrow "tilted ring" of swept area of travel reduces the load they dare apply when NOT on a decent live center, before they are galling and ruining the socket, most common materials, from too stingy a contact area.
The Old Skewl trick if you had no such critter - or had just trashed one - was to grease-up a bearing ball and run it in a cup center.
Given it ain't hard to gather a suitable collection of those hardened bearing-balls, some among us figure the fallback is actually easier to support with clean and undamaged goods than the bespoke ball-end center tip is.
Back to the question: If a precision GRINDER is the horse you wish to saddle, not just vanilla lathe work?
You will want to meet or TRY to beat the primo maker's of store-bought dead centers who do it as Day Job.
See Stark, Riten,
et al for their current specification's and pricing.
If/as/when the specs have gotten tighter and better over the years? Well.. the folks USING them have had reasons to pay for better goods.
Truth, is I keep my one of each "top end" ones set aside for measuring and assessment of the lathes. I don't USE them for actual turning atall.
Ordinary work I use bog-standard commodity centers, carbide tipped, some of them even Chinese-made. Cheaper and easier to keep reminding myself that dead centers never WERE going to last "forever".