- think tank funding
- ad spending
- lobbying (CF will not fix that)
- the potential of future jobs / revolving door
Most importantly, cultural deference does not go away with CF reform; people respect the monied and the powerful for more than their campaign contributions. They also respect people "like them" (http://time.com/373/congress-is-now-mostly-a-millionaires-cl...), which means similar socio-economic backgrounds, elite schools, clubs, etc.
They buy influence indirectly by simply having wealth and power concentrated with them. You can only reduce that by reducing the distance between the bottom and the top. You have to reduce "vertical social distance."
Nothing is a silver bullet here, but reducing wealth inequality is the most direct route to equalizing political power.
https://en.wikipedia.org/wiki/Elite_theory
https://en.wikipedia.org/wiki/Iron_law_of_oligarchy
I especially recommend reading "The original problem of social distance" in "Twilight of the Elites."