I tried to make one a time or two - with varying degrees of success; I believe my imprecision in cutting the arcs was at least one issue. I think the answer to that issues in have the plates made with a CNC; several here were willing to do that for me, I just never followed through.
My turning has declined for varous reasons, in PART due to the fact the I was never able to get a 'decent' 'finish the bottom' solution. Even longworth chucks are universally applicable - as I believe these would only work for a smooth edged bowl, or platter, not likely for a natural edge bowl. I think a for which I think a vacuum chuck would be the most generally applicable.
Commercial Longworth chucks are available, as I recall handling them at some Klingspors show a few years ago. They weren't inexpensive ($85-150 IIRC??? Correction these are $160-280 for the two sizes) for various sizes, and while I thought those were reasonably well made, I chose to spend my $$ elsewhere. I may still purchase some day.
I also had no real success with Cole jaws, but maybe I forget what those were...