Why do we want a RH bat off the bench when the only starters he would be replacing are already RH? Your bench should complement the starting lineup, not fit some model that says you need a certain handed bat for specific situations. Which LH bat do you pull late in a game for Millar? Not Ortiz. Not Drew. Maybe Ellsbury. Certainly Cora. How often does Cora come up late in the game needing to be PH for? And, now that Bailey is up, why can't he do it. He's got more pop than KFK.
As for being more productive than Casey. Millar's OBP is .337 to Casey's .412. From a bench guy, I'll take the far fewer outs over the extra bases. As for Casey maintaining that going forward, what makes you assume he's got to drop off? A hunch? His OBP by month is as follows: .424, .391, .392, .424, .409. Casey handles the bat well and has a good eye. It looks like coming off the bench suits him as he doesn't have to suit up to play every day and get worn down. Also, he doesn't hit many XBH's, not according to his stats he doesn't, but for those that like what their eyes tell them, how many of his hits did you think "double" off the bat? He's a slug. He makes Lowell look fleet of foot. The benefit of the XBH isn't limited to the hitter. The balls he hits into the gap still move the other runners over according their speed.
Let's review. He's LH, the opposite of Youk and Lowell. He handles the bat well and hits for a high average. While he has no range, he's one of the most sure handed gloves in the game at 1B, a position where range is not as important. And he's capable of having stretches of time in between ABs and still producing. Casey is ideal for this team and its current roster.