Just about every pro sports league needs to manage its rules to ensure that the playing field gets leveled every season. For example, NFL draft picks are in reverse order of season success. If last year's Super Bowl winner was able to choose their next team on a completely free market, they would simply use their boosted revenue and pay the most for the best players, thus making it much more likely that they'll increase their domination. No one wants to watch a dominating team shut out clearly inferior teams game after game.
F1 needs rules to tighten gaps between the team and to prevent one team from spending their way to success. I think we can argue about whether the new power units, DRS, and tire management are the right way to do this, but I'm glad they're trying something.
Outside of America there are far more sports that don't try to even the playing field artificially. Motor racing (I don't know much about non-F1 racing anyway) is pretty much the limit in the UK, team games generally work on the free market, individual games can generally be dominated by great individuals.
FFP is generally considered slightly better than nothing, but only just - it's a joke. It's talked about as if it will stop clubs like Man City and Chelsea dominate financially, but it only affects TV money, not any other sources of income (e.g. sponsorships), so realistically it is going to have hardly any effect. Even if it was implemented in a stronger way, it would still only serve to bring football closer to how it was 20 years ago before big money owners were so prominent, it would never take it to a US-sports level where they try to balance teams out completely.
The foreign player rule is about trying to boost national players rather than international players and has nothing to do with trying to even the (metaphorical) playing field.
F1 needs rules to tighten gaps between the team and to prevent one team from spending their way to success. I think we can argue about whether the new power units, DRS, and tire management are the right way to do this, but I'm glad they're trying something.