Yes, I am refering to single player too, and even more so to the career mode.
I totally get your gut feel about a gain being required to incentivise qualifyings (P4 as best possible choice if you don´t run qualifyings might be that incentive, like you said before).
But you kinda sharped your point towards the end … it´s rather about the fear of slowing down your progression, because that´s what we are used to from other games.
It would be very important for the game to communicate the freedom to “play however you want” while always making roughly the same progress.
The XP (Time, Miles driven) -based progression idea feeds into that.
Same with my suggestion for an endless, procedual career mode. (Endless Career)
Once there is no huge checklist of events you need to work through to “finish” the game, there is no stress about getting those checkmarks or gold medals or whatever.
Which in turn should allow our brains to feel free to run Qualifyings without losing out on anything.
Sorry, just having fun toying with thoughts and ideas.
Imo there´s a lot of systems interacting with the implementation of Qualifyings, at least if Turn10 want to keep their broad audience.