The only reason he wouldn’t do is may want to spare his gold goose’s “Carr” feelings. If Rattler is the backup Carr may get in his feelings when everyone starts calling for Rattler.
Or he doesn't want to put too much pressure on a rookie QB and wants to give him time to develop without all the expectations building around him. In the end, it doesn't really matter who the #2 QB is. Carr is going to start as long as he is healthy and if he's hurt for any length of time, the season is pretty much so over. I think Rattler is going to be very good, but he still needs time to develop.
That being said, I could see a situation where Haener is brought in after a Carr injury if you have the lead and Rattler might get the nod if they have a week to prepare or you are behind.