The reason why Diaz makes sense for the Yankees is because in Brett Gardner and Curtis Granderson they have two outfielders who struggle a bit against left handed pitching. One thing Diaz does very well is hit lefties. Last season he had a .830 OPS against southpaws and over his career he has fared even better putting up a .907 OPS over his career.
The one thing that will come into play here is playing time. The biggest things that come into play when it comes to bench pieces are how much money they will make and sometimes more important is how much they will play. Over the past few years the Yankees haven’t really had a lot of either to offer to potential bench pieces.
Last offseason they offered the bare minimum for their reserve outfielders eventually settling on Randy Winn for $1.1 million and Marcus Thames on a minor league deal. Then during the season Winn barely played and was eventually cut. Thames got playing time, but almost none in the outfield and only at DH because of injuries. Even Austin Kearns, the other backup outfielder they brought in, hardly played at all down the stretch and not at all in the playoffs.
So while the Yankees may be interested in Diaz, it’s unlikely that they are going to outbid anyone for him and he has to come in knowing he might not get a lot of playing time. If Gardner or Granderson struggle against lefties he’ll get some time, but even then almost any National League team will be able to offer him a better situation.