For the benzene thing, comparing benzene to cyclohexadiene isn't really a "fair" comparison because they have different numbers of bonds, right? Benzene: 6 C-C sigma bonds, 3 C-C pi bonds, 6 C-H bonds. Cyclohexadiene: 6 C-C sigma bonds, 2 C-C pi bonds, 8 C-H bonds. If you compare benzene (with resonance) to cyclohexaTRIene (assuming no resonance) then the difference you see is the resonance stabilization energy only, right? I guess you could do the same calculation from cyclohexadiene, but you would just have to account for a lot more energies in the process.
For purely covalent compounds the neutral form should always be more stable than the charged form. I can't think of a contradicition of that. There are some compounds that are stable but have some sort of charge separation within the compound, but overall their charge is 0.