Note that I haven't used such a VFD, nor had I felt a need to slow down my grinders. But since that was the question, and I'm aware such VFDs exist (and are affordable), I decided to post about it.
I wouldn't be so sure about cap start / centrifugal switch. According to a manufacturer of single-phase VFDs,
"Connect VFD's U, V, W phase to induction motor's terminals correspondingly as show in following wiring instruction (The capacitors of single phase motor can be removed if necessary)."
Search for "Wiring a VFD to control single phase motor speeds" to find this page with a connection diagram, I can't post it, since I don't have 5 posts yet.
But maybe you're right about cap starts being out.
Invertek says their single-phase output VFDs are suitable for "PSC (Permanent Split Capacitor) or Shaded-Pole Single Phase induction motors".
Leeson says "Permanent split capacitor (PSC), Shaded pole, and AC synchronous."
So, capacitor start would be not suitable, however capacitor run (=PSC) are suitable. I've seen grinders with motors of both types (e.g. my 1998 Elektra Beckum DS200W is cap start, while all their lower power models were cap-run).
I have heard some people claim they have converted cap-start motors to cap-run (replace centrifugal switch with a jumper, replace the start capacitor with a run capacitor - those are rated for continuous duty and are lower in their capacitance value) and had those motors happily running for years since. Feels more like a hack, though.