1) Avoiding the "turtles all the way down" problem of recusal following recusal.
2) (More likely) Because the next person up after Rosenstein is Associate Attorney General Rachel Brand. Brand is problematic for a number of reasons. First: She doesn't have Rosenstein's extensive prosecutorial experience - she's a political lawyer. She actually has no prosecution experience at all. She's just got a Harvard JD, the right clerkships, and gone back and forth between big name firms and legal positions with Republicans. In short, she isn't qualified to oversee a national security investigation like this. At all. Rosenstein was US Attorney for Maryland for a long time, and has a reputation as a very solid prosecutor. Second: She was involved in the Bush Administration US Attorney firing scandal (the same one that gave us Alberto Gonzales saying "I don't recall" seventy-some odd times in one hearing, and resulted in White House DOJ liason Monica Goodling having to receive immunity from prosecution and getting reprimanded by the Virginia Bar). Specifically, Brand was going to replace one of the US Attorneys who was going to be bounced for not grinding political axes by means of criminal prosecutions. The Bush Administration thought she'd be more inclined to base her decisions on politics than evidence.
Does this sound like someone who should be overseeing a probe of this magnitude with huge political ramifications?
Oh, and also Rosenstein was almost certainly interviewed by the agents/prosecutors in the Mueller probe, and they would have raised a stink if they had a problem with him staying in the loop. My guess is that he went over the letter he wrote about Comey and his reasons for writing it.
"There's no play here. There's no angle. There's no champagne room. I'm not a miracle worker, I'm a janitor. The math on this is simple; the smaller the mess, the easier it is for me to clean up." -Michael Clayton