I do agree, I have exactly the same principles and I guess that's why the QP is my daily driver. I wanted to explore its limits and there's nothing better than the track for that. I took the Gransport back then and it was working quite well too.
The QP is clearly not designed for the job because of its weight. The idea is to hammer it for 2/3 laps and do a cool down lap and go at it again. On the other hand, a McLaren 570S isn't a track car either. In fact, no street car is really designed to be driven like a race car (even the 911 GT3s and GT2s and the 488 Pista, etc.). I do agree the latter are a bit more purposeful for that but you'd be better off driving a Challenge car or a 570 GT4 (or whatever is the newer one), or any race car - actually many cheap race cars will go faster than street super cars if their power to weight ratio is good enough and mainly because of the fact you'll brake at 50m from the turn versus 125 to 150 in a street car, plus you carry the extra weight around corners too...