I think your supposition is almost certainly correct.
Fundamentally, the RP10 has no character. It is a blank sheet of paper, or as close to it as I've ever heard a record player get. My understanding is that the P8, and the other 'plastic' decks, are similar but the P8 has slightly more warmth about it? Most turntables add quite a bit of their own colour and it generally helps give you that likable vinyl sound.
I thought the neutrality of the RP10 would make matching easier but it doesn't. The majority of cartridges are balanced to work on typical turntables, not ones as clean as the Regas. While the Exact has sins of omission, it's the first cartridge I've tried that I feel does nothing wrong. Or rather the vinyl set up as a whole is doing nothing wrong. It lacks a little 'air' but it's not as chronically 2D as cheaper Rega MM carts. It sounds clean, detailed and fast but has enough weight and warmth to fill in what the RP10 lacks. It's sounds....right.
I don't know how big the gap is between the P6 and 8 but the margin over my LP12s is big. I ran LP12s with Norton, Valhalla and Avondale PSUs. Circus and pre-Cirkus bearings, almost all Linn arms up to the Ittok and modified Regas. A lot of carts up to Troika and OC9. The RP10/Exact lets to see how trivial all of those changes were. Just tweaks this way or that. The Rega is a fundamental shift upwards in almost every area. It sounds like what you think a high-end turntable should sound like.
Obviously lots of people are just as happy using better Rega carts and I'm not suggesting they're wrong. It's really just a question of getting the right balance in your particular system. Thirty years with the LP12 meant everything I had or had done was optimizing that particular sound. The Rega has sounded wrong for a long time. I think that's why a lot of people reject them, they don't realize how much they might have to change to get the balance right. But it's worth the effort as it's a cheap, simple way to get really high sound quality.