Money definitely sways elections.
The few case where it doesn't are normally attributable to other problems with the spendy campaign.
In Wisconsin, the conservatives spent enormous sums of money talking about high level worldview issues like DEI and immigration. Which is all well and good if you're in a state where that's relevant maybe? But out here in opioid infested flyover country where people were worried about losing their housing the next week, those worldview kinds of things were just dumb issues to focus so much money on.
So yeah, you can win an election against a big spender. But normally that big spender is actually so dumb and detached from the voters that what's really happening is that they're beating themselves.
American politics for all intents and purposes is a very simple game.
Similarly Mamdani in NYC is facing some truly awful candidates.
Someone also pointed out to me that it's not so much the money on a politician's side that sways them, but the threat of PACs et al spending a ton of money to unseat them if they don't "play ball". [2]
[1] https://www.independent.co.uk/news/world/americas/us-politic...
[2] https://www.opensecrets.org/elections-overview/winning-vs-sp...
I think you're thinking about this in the wrong way.
What you're saying is that people who don't have a lot of money to spend usually don't make it to the election.