Foreword (and I'm late to the party on this one), I haven't played much of PoE2 due to waiting on the dlcs, but I don't think in general there's anything wrong with retaining the protagonist across multiple rpgs. The BG series is very memorable for me specifically because of the rising stakes, returning PC and companion characters I grew attached too. Similarly in recent years, if the stars had aligned and we'd got a proper Dragon Age sequel with the warden PC that continued their story with select returning characters, I'd have been a happy camper.
But as has seemingly been brought up in recent Pillars threads (only scanned them, they've been moving at quite a pace) one of the core issues I had from the onset of Pillars 2 is even though I was getting many of the things I'd want in a BG/DA "proper" sequel, PoE1 was simply... mundane, boring in many aspects. It was very clear to me that it was produced by remnants of the Icewind Dale crew who were trying to emulate elements of BG to varying degrees of success. But succintly put, after PoE, I had very little attachment to any of the cast; Eder a little, maybe, but by and large, they were just supremely unmemorable.
I'm not sure a new PC would have fixed that and to be fair there was fuck all character development of the BG1 companions past their initial introduction and a 1-2 line complaint if you didn't go where they wanted within a set timeframe; all development came in BG2. So in that regard, Pillars 1 was on better footing than BG1, but it only ever felt like a BG1.5 to me. The game just has this inherent flaw of me just not caring about anything that's transpiring, and in the interim we'd had Dragonfall & D:OS2 which caught and retained my interest throughout. Pillars just lacks... something and I don't know how you could fix it (even though I actually find the world and background lore in Pillars more interesting than some of the other games I've cited, the first game was just... eh).
*All that said I did start a replay with IEMod and disabled all the Gold-Backer NPC shit and the pacing improved dramatically, so the plethora of inconsequential backer content probably contributed to my disconnect with the game. Carry on!