The way I see it, the only reason political parties need such vast amounts of money is to spend it campaigning. If you reduce the need or ability to campaign, by restricting advertising or making voting compulsory, the demand for money is lessened, and some industry or another threatening to pull their support isn't such a big deal.
A huge part of campaigning is either driving your own turnout (field operations) or suppressing the other guys' turnout (negative ads). Additionally, there's a philosophy of "suppress turnout in general and it will probably help me", which statistically is a good move for Republicans, most of the time.
The argument is that compulsory voting would disincentivize these activities in favor of issues-based campaigning. I agree although I'm not sure I agree strongly enough to favor compulsory voting.
You want to contribute money to politics? Sure, feel free to pour some into this big barrel over here. The proceeds will be evenly divided between all candidates.
