IME the main benefit of a periphery ring and center clamp was mentioned by Narrod: better coupling of vinyl to platter. This helps drain or dampen intra-vinyl resonances, which lowers the sound floor and improves the clarity of everything.
On my rig (not a VPI) resonance management was a much greater audible benefit than warp flattening (not that warp flattening was unwelcome). I used my ring whether the record was warped or not, always to good effect.
There is some risk of course. You have to pay attention while cueing.
Doug
P.S. You can use a center clamp without a periphery ring, but usually not the other way around. If you want to get some idea of what a ring would do without spending for the ring, try the center clamp alone. IME it will provide about half the benefit of using both. If you're getting ANY slippage of record against platter due to stylus drag, the center clamp will prevent that and provide an even bigger bang for buck. IMO a center clamp at a minimum is essential with platters that don't use a soft mat.