The lack of 3rd parties is not a function of spending - it's due to one-winner voting. With only one winner in each election, voters who would prefer a 3rd, 4th, or 5th place candidate quickly figure out that this is a waste of time and they had better line up behind one of the top two. This is how the US does end up with a small handful of 3rd party candidates here and there - because there were enough concentration of voters in their (usually small) district to make them the top candidate in that district. Very hard for smaller parties to have this level of concentrated support over any medium or large area.

An alternative voting system might have voting for many offices together, with many winners. In that case the winners can be distributed among the various voter preferences proportionally. Some countries already do this and therefore have reasonably robust multi-party systems - though I don't think it's at all clear that this is better at serving the needs of the public.