Obviously, a season of data will be needed, but my initial feeling is that the new DL rules will enhance predictability in player value, and will ultimately have a slightly positive impact on owners being able to reach GP and IP limits.
My rationale for that belief is that players ended up playing hurt more often with a 15-Day DL, they rush themselves back from a day to day injury to avoid being shelved for 15 days. A great example is Yoenis Cespedes last season, who missed 4 games with a quad injury, came back too early, his OPS dropped 44 points, and he ended up on the 15 day anyway a month later. If there was a 10 day last season, he probably ends up playing more games in 2016. He probably ends up with a better statistical season too, because his play fell off significantly while with the quad injury.
I can only think of one player this year where the 10 day DL has actually had an impact, Jean Segura. Minor hammy issue, this year, he comes back and hits a HR in his first game back. Last year, Segura may not go on the 15 day DL with that injury, maybe he rushes back after five or so games this year if there is no 10 day, maybe he never gets back to 100% or ends up with a prolonged DL stint later in the season.
A 10 day DL stint for a pitcher like Kendall Graveman is essentially meaningless to his value, as he would have just had a start skipped last year, just no DL. The new rule allows more players on the 40 man to make a big league impact.
I don't see how the new DL rule ends up having an impact on the value of an under-producing multi-position player like Profar, or Reyes who are likely bad starts no matter what position you are starting them at this year. Maybe some owners will panic when they see the red "DL" next to their player's name and dump mediocre prospects for utility guys, but maybe those those prospects should not be rostered in the first place, and those moves signify an inefficient roster. It may end up having a negative impact on utility players because teams will inevitably create 40 man depth charts, and stash backups in AAA rather than on the big league roster.