easy answer:
private license = you pay to fly
commercial = you are paid.
Easy? Yes.
Correct? No.
You do actually understand what a pilots license is, and that they come in various grades, yes?
You cannot be a pilot in a commercial operation with a private license, no matter who is paying what.
As to the rest, as has been stated, responsibility does not change. A Private Pilot paying to fly a privat aircraft still bears the same responsibility for the safe conduct of his operation as does a commercial pilot.
P2F sucks. Just not for any of the reasons you've stated.