I did a quick survey of the 4 unowned teams in one of my leagues.

What I found was about 15 players that I would classify as stars or future stars. I also found about 60-65 players I would classify as "decent regulars." These are players that are not stars but could fill a regular role as a position player, starter, or closer with a level of performance high enough that it likely would not harm a team.

The total player pool was 144 players.... At least 30 of these players have negligible value.

This is only one sample of one league. However, if this example was typical then I would say a reasonable way to inject life into the bottom teams in a league is to implement the following --

Contraction Draft of 7 rounds. The "order of each round" is similar to a rookie draft with the following modifications.

Rounds 1-2: Only the worst 8 teams in the league draft [ 2*8 = 16 players ]
Round 3: The worst 12 teams in the league draft [1*12 = 12 players ]
Round 4-7: All teams in the league draft [3*20 = 80 players]

Total Drafted Players = 108

With this system almost all of the useful players get drafted, the top 24 players go to the worst 8 teams, and the top 28 players go to the worst 12 teams.

The top teams still have a chance to pick up a 5th starter, a #8 hitter at a position of their choice, or a reliever --- but they won't get the stars.