Perhaps it would make it easier to rebuild if the roster cuts were totally dropped - cut to 35 ONLY after the FA draft.

A rebuilding team needs to gamble on players making it, young pitchers particularly are unpredictable. Being able to keep a large number of promising rookies helps your chance that some will have breakout years.

Meanwhile...a strong veteran squad has players that are very predictable so cutting to 27 is not that big a deal. Sure you may have to give up some promising youngsters (and pick up some of them again in the FA draft), but you can rely on your core players.

For instance:

A roster of:
Ivan Rodriguez - C
Todd Helton - 1B
Jeff Kent - 2B
Eric Chavez - 3B
Jimmy Rollins - SS
Tory Hunter - CF
Barry Bonds - LF
Valdimir Guerrero - RF
Roger Clemens
Curt Schilling
Jason Schmidt
Pedro Martinez
Mariano Rivera
Eric Gagne

and you can cut to 14 and still expect to challenge for the title for many years (replacing guys as they age).

Meanwhile someone rebuilding with a roster of promising young players but still unproven, will be forced to cut players critical to their hopes of success. Those players then become available to the strong teams in the FA draft. Suppose you are a rebuilding team and trade for extra rookie picks. You just have to cut them before the FA draft (or someone else on your roster you like) so extra rookie picks lose their value. Perhaps they were better than the FA picks you ended up wish, you don't have a choice. If you didn't have to cut unitl AFTER the FA draft, you could either keep your rookie picks or your FA picks depending on which you preferred.

In addition, strong teams aren't necessarily stronger for players 28-35 than a weak team, they are stronger for players 1-15. A weak team may actually be much stronger for players 28-35 where they are stockpiling prospects.

After the cuts, everyone has an equal chance at the FA pool. The cuts hurt the weak teams more than the strong teams.