My thought on how to get contestants to stay and play
Every season The Floor introduces new things to try to encourage people to stay and play, although none of them seem to appreciably improve the odds of winning. First it was the $20k to whoever has the most territory at the end of the episode, then it was the Time Boost, then the Category Steal, and now the Territory Freeze. Based on who the winners have turned out to be every season, it appears that the most effective strategy is to have a niche category that nobody wants to challenge and stay on the floor as much as possible. I think that there is a change they could make that could potentially improve the odds of winning for those who stay and play enough that it might actually make sense to not immediately go back to the floor.
I think that instead of the Time Boost, they should give a player who has won 3 duels the option to have a Life. A player with a Life who loses a duel would be able to stay in the game, but would only keep one rectangle. The rest of their territory would go to the winner. Players who don't lose should be able to keep accumulating lives. I think the longest winning streak so far has been 7, so it seems unlikely that a player would accumulate more than two.
Right now not playing tends to be the winning strategy because every time you play, there's a chance you could lose, and if you lose once, you're out of the game. With Lives, there's still a chance you could lose each time you play, but losing once no longer necessarily means you're out of the game. This would provide an advantage in particular to very good duelers who stay and play and keep winning.
I think the biggest problem with Lives is that it would make the game take longer, and they only have a finite number of episodes. My preferred solution for this would be to cut out the reality TV-style confessionals and just have more duels each episode, but if they're married to the confessionals, they'd probably have to introduce something like doubles duels in the back half of the season to eliminate two players at a time.