If the worst current players got cut then yes, though the high levels would still generally be the same, your bottom 2 teams full of the worst players would just all be removed along with the teams. But teams will be cutting the worst prospects which isn't the same as the worst player. Some bad veteran in AAA who a team no longer wants will get cut over the 8th round draft pick from the last draft who's in the FCL. The AAA cut will almost certainly be a better current player than everyone on the FCL roster, but those lower guys have potential so will be hung onto. Once a bunch of these holes are made at the upper levels guys who would normally be in the lower levels if we had 8 affiliates now need to get pushed up to fill holes watering down the entire minor leagues as a whole.
Just look at where newly drafted College players get sent these days. Under the old system most of them went to Vancouver(Short Season A). That doesn't exist anymore so they either have to go to the FCL(lower level) or Dunedin/Vancouver(Higher level). Just about every College guy we drafted last year started in full season ball. That level is weaker than it used to be.
As an exercise pretend every minor league team was getting deleted except AAA and AA. You only got to keep 50 prospects, send 25 to Buffalo, and 25 to New Hampshire. Everyone else is gone. There's a bunch of lower level guys you're be assigning to New Hampshire because you want to keep them for their MLB potential, and AA would be a hell of a lot weaker than it is now with guys like Irv Carter, Pinto, Beltre, Meza, etc, etc playing there. It's an extreme example, but going from 8 to 6 teams like they did within the last couple years would follow the same principle