This isn’t really “ladder” … more accurately a survivor format. Because you’r’e trying not to get eliminated, and you don’t have better-qualifying seeds joining the ladder matches after a number of worse-qualifying seeds have already survived.
Nearly this exact format was used in at least one tourney in TX a number of years ago (I believe Houston Expo, before @spraynard took over running the Space City Open there). Yes, it saves time, but it was not very popular. I wasn’t attending – I only heard the stories.
Generally speaking, you don’t want to spend a relatively long time, over the course of MANY games qualifying for a finals, only to be one-and-done – particularly for those that earned top/best seeds. So it depends on what type of games that could be used for the potential one-game-and-done finals. In the example I’m referencing, some luck-box 2" flipper EM’s were used extensively. To make matters worse, in my referenced example, I believe that the eliminated player got to choose the next game for their surviving group. (madness!)
If you still want to give this format a try, I’d suggest providing the top 4 seeds one bye, and have Round 1 that 8-9-16, 7-10-15, etc. play one 3-player game each, with 2 players surviving each game, and seeds 1-4 joining their respective surviving twosome for round 2. This way, there’s even more incentive to finish in the top 4.
For game selection restriction, I’d say that once the best seeds have joined the fray, each group cannot play the same game twice in the Mini-Ladder portion. But players may once again have a “clean slate” of game choice starting Round 5.