I agree with what you're saying but think you haven't considered the correct counterfactual.
Right now we live in a world where candidates raise oodles of cash. Why? Mostly to pay for marketing and media pushes. Money gets you TV ads, radio spots, etc.
Let's say we wave our magic Citizens United wand and heavily restrict campaign financing in some way. Restrict how much they can raise. Restrict how much they can spend. Restrict where they can get money. Doesn't matter, just imagine that the end result is that candidates raise a few million instead of a few billion.
What happens now? You hit the nail ont he head right there
> Overall this is not a problem in the USA alone if you have the media/papers on your side the chance of winning an elections grows exponential.
The media is biased. It's biased because it's ultimately run by humans and humans aren't robots. Media owners have politicians they favour. Media employees have political leanings.
Right now, in a world with essentially unlimited campaign spending, this media bias largely doesn't matter, because they are more than happy to take any politician's money in exchange for ad space
This changes in a world where politicians can't spend enough money to buy ad space. In this world, who gets the TV spots? The people with connections. The candidates leverage personal friendships and ideological biases to get "heavily discounted" airtime while the less well connected, or less institutionally popular candidates get nothing.
We all look at campaign financing and see the bad parts, but consider the alternative. In this world, Sanders can still run TV spots because he can crowdsource money from grassroots sources and pay what ads cost. In a world with that door closed to him, all he can do is fall back on connections and hope for the best. And for someone for whom being an outsider is so core to his branding, I wouldn't count on those connections to amount to much