Contrary to some state-level efforts and laws; companies are not people.
This kind of stuff is why I see America more as a corporate oligarchy than a democracy anymore. Gerrymandering, lobbying/bribery, and lack of contact with our government means it doesn't represent the people any longer.
The problem is that political success in the US depends on a successful marketing & sales campaign, which in turn costs a lot of money. Legislating campaign events out of existence seems to be a non-starter, but with a progressive supreme court paid political advertising could be curtailed or stopped, in return opening up debate and equal-time promo slots on network TV that uses licensed slices public airwaves. Journalists and opinion-swayers could still report on candidates as they did before, but the need to have millions of dollars to run a senate campaign would be dramatically reduced. Of course there's a big free speech juggling act that would have to be performed, but it's not an insurmountable problem.
Couple this with some relatively lightweight voting reform (IRV or something more sophisticated, plus data driven auto-districting or even proportional representation at a state level to combat gerrymandering) and a good deal of the problems with the system go away, since politicians would have to spend much less of their time seeking donations (and politicians who were still doing a lot of fundraising would stand out more and could be investigated more thoroughly.)
Our current system predominantly favors white, rich, cis-gendered male christians who are good at manipulating their constituents and getting rich people and corporations to give them money. This seems like such an awful set of criteria that it is hard to see how just picking randomly could fail to be better. (There is evidence that sometimes it is better to choose randomly than relying on ineffective criteria: https://www.theguardian.com/lifeandstyle/2014/oct/10/random-...)
Even if you eliminate the problems of campaign finance and winner-takes-all in elections we are still left with the distorting incentives of re-election (though enforced single terms could help with that.)
State representatives that want to be successfully re-elected, need to bring home the pork and this incentives wasteful government spending. They also need to avoid taking political stances that might cost them the election, even when it has popular support and would be beneficial to our society (e.g. gun laws, criminal reform and the legalization of marijuana).
Removing perverse incentives of re-election and moving to random selection for one of our chambers of representatives would mean less pointless pork barrel spending, reduce the incentives for corruption, and lead to a more representative demographic sampling with a better personal understanding of the economic and social challenges we face as a society.
Certainly a risk, but we have already have a similar shadow government of congressional aids and special interest lobbyists today. I think this can be mitigated to some degree by providing funding and resources for self education, but this is something that would need to be taken under consideration as the system was designed and measured as the system was implemented.
1) Donations to politicians from companies/foreigners need an absolute ban.
2) Personal donations should be capped at what a average politically interested person could afford.
3) A company can either lobby or hire government employees, not both. If a company lobbies government they cant hire senior government employees for 7 years. Likewise if a company hires senior government staff they cant lobby for 7 years. This way if a business is lobbying government then that person knows there is no cushy job for them at the end and your not hiring someone for their relationships that can directly influence government.
I know these will have loopholes and need more detail etc. Not least super pac issue in US (I am Australian so different challenges). I do believe something around this framework would significantly change the face of politics towards working for their constituents. Especially with the internet today and its ability to spread information and ideas.
IMHO, if it weren't for reddit, imgur, news.ycombintor, etc. Net Neutrality would have been killed the first time. Now Ajit is just hoping that if the battle is drawn out, we'll fatigue, and he won't be eviscerated by his corporate overlords. And, unfortunately, he's probably right.