It kinda depends on how rewards are handled. If you are rewarded just based on the wins that your submitted deck does, then there's basically no reason to do anything but play at the highest level you can, at least as long as it takes at least a day to get eliminated from the league from a new submission. Higher level presumably means higher chance of winning, and is stated to mean more monetary reward. If this is the case, might as well allow people to submit to whatever they want.
If reward is based on league standing, though, it should probably be prohibited to submit to lower leagues, as anyone below the top levels will be at a strong advantage, and there will quickly be a (more severe) rich-get-richer situation.
I'm leaning towards voting overall to restrict people to be in whatever league they are actually supposed to be in score-wise. For the people who refuse to be at the bottom of a stronger league in favor of being at the top of a weaker league, they can begin and resign a few FG games or something to drop their score quite quickly.