You don't need a complete ban, just sensible financial limits. In the UK, campaign spending by political parties must not exceed £30,000 ($38,000) per candidate. That's enough money to inform potential voters of your policies, but little enough to reduce the influence of money in politics to a minimum. The EU referendum was highly controversial because some campaign groups may have spent over £15m ($19m) nationally, which I understand is chump change in the US.

https://www.electoralcommission.org.uk/i-am-a/party-or-campa...