What the free market rules should be are fairly clear. When corporations influence government to favor those corporations and blunt competition, that is not a failure of the free market, it is a failure of the government.
But can you have free markets if corporations are permitted to influence the government? It seems impossible; humans will be influenced by those with whom they have contact.
So the alternative is to prohibit corporations from lobbying government, but that would be tantamount to removing legal personality from corporations and it is questionable whether the result is a free market system. You would also need to remove the right of people to lobby on behalf of groups of other people, and it is questionable whether the resulting system is free at all, or in any ways desirable.
The system that we have approaches free market capitalism as well as a liberal system can.
You can never have a perfect free market, nothing that humans craft is ever perfect. But you can get pretty close. As I've posted here before, the software development industry is fairly close to a free market.
Besides, just because we cannot reach perfection is not justification to run the other way. The government is run by people, and people are subject to imperfection, incompetence, and corruption. The more power added to that means the more temptation there is to use that power for personal agendas.
Remember that county clerk who was using her government power to deny marriage licenses to gay couples?
Only a select few win big and often their products are way overvalued. The road to billion valuation is littered with dead startups doing almost the same thing.
The economy in general and government were quite disjoint for a very long time. This was considered an active goal to be pursued.
The arguments for changing that were largely of a Progressive (by the timbre of the times) nature - trustbusting and all of that. I don't think that genie can be put back in the bottle.
Not true, wealth accumulation is sure to happen in a free market due to random circumstances and just even minimal imperfections in knowledge. Government is not required.
And a wealthy player would be a fool to not try to skew the rules in their favour.
Nobody has proven yet that it is possible to prevent this problem even in a really long term.