It seems you are mixing the concepts of voting systems and candidate selection. FPP nor FPTP should not sound scary. As a voting systems, FPP works well enough more often than many want to admit. The name just describes it in more detail: First Preference Plurality.
Every voting system is as bottom-up or top-down as the candidate selection process. The voting system itself doesn’t really affect whether it is top down or bottom up. Requiring approval/voting from the current rulers would be top-down. Only requiring ten signatures on a community petition is more bottom up.
The voting systems don’t care about the candidate selection process. Some require precordination for a “party”, but that could also be a party of 1. A party of 1 might not be able to get as much representation as one with more people: but that’s also the case for every voting system that selects the same number of candidates.
Voting systems don’t even need to be used for representation systems. If a group of friends are voting on where to eat, one problem might be selecting the places to vote on, but that’s before the vote. With the vote, FPP might have 70% prefer pizza over Indian food, but the Indian food vote might still win because the pizza voters had another first choice. Having more candidates often leads to minority rule/choice, and that’s not very good for food choice nor community representation.
You should probably read/know the actual law, rather than just getting it close. You’re probably referring to 18 USC 922 (d) (10), which includes any felony-- not just shooting. That’s one of 11 listed requirements in that section, which assumes that the first requirement (a) (1) is met: not an interstate nor foreign transaction. There’s a lot more to it than just “as long as you don’t have good evidence they’re going to go shoot someone”
Even after the sale, ownership is still illegal under section (g)-- it just isn’t the seller’s fault anymore.
This is basic information that should be known to any gun safety advocate. “Responsible” gun owners must know those laws, plus others backward and forward. One small slip-up is a felony, jail, and permanent loss of gun ownership/use. Are they really supposed to listen to those who can’t even talk about current law correctly?
The law can be better, but you won’t do yourself any favors by misrepresenting it.