When I first saw this spoiled, I was excited, as Mirāju looked like it was bound to be how Jinteki decks would mitigate agenda flood; but with some testing and the UFAQ, this potential really hasn't been met.
Problem 1 - The runner won't run
Mirāju, as a piece of ice, only triggers if the runner actually runs it, which means if you draw into too many agendas, you need to hold onto them until the runner runs into it, which still leaves you stuck with the several turns of operating at minimal efficiency, as you are forced to do things in the wrong order, or just accept that you'll be discarding valuable cards.
Problem 2 - The shuffle isn't optional
Mirāju looks like it was written to give the corp the choice of drawing and shuffling, or doing nothing; but the UFAQ says the corp doesn't need to draw to shuffle a card away, so you have to do so, no matter what.
This is a pretty severe downside, as it if the runner has some multi-access, such as with Medium, or R&D Interfaces, an easily accessible Mirāju is a death sentence, as the runner can easily run into it to force a shuffle for fresh accesses.
Problem 3 - Low value on other servers
Primarily as a result of the shuffle not being optional, Mirāju is pretty low value on servers other than HQ.
- On Archives, the runner can happily break Mirāju, and laugh at you for even rezzing it, unless they are stuck with Black Orchestra, or you have a Crick or something in front of it.
- On R&D, Mirāju provides a way for the runner to get fresh accesses, especially if they have multi-access.
- On remote servers, you really want ice that can help you score your agendas, and this does nothing to help with that.
Problem 4 - Mirāju doesn't help against Account Siphon
Miraju doesn't do anything to stop the runner siphoning you into the ground, so you either need additional, normal ice on HQ, or you need other cards to help protect you from siphon, like Crisium Grid.
Problem 5 - Install costs add up.
Miraju is not as cheap as it appears, 2 credits sounds cheap, but it's not the whole story.
Miraju, purely by being a piece of ice, adds to the install cost of other ice you install; which if you want 2 or 3 other ice on HQ, it will easily cost you an extra 2-3 credits.
Miraju is pretty good for keeping you from losing agendas out of HQ, but it's value is so narrow that it's simply not practical to use for much else, and even for protecting HQ, some normal taxing ice is often going to be similarly helpful.
This is further made worse by the fact that Miraju is the kind of ice you want to see early, but with only one good place to put it, including 3 of them is bound to result in not drawing suitable ice for other servers, or drawing them late game with more than enough ice on HQ already.
You could probably run a couple of them in most Jinteki decks, but most of the time, two or three triggers of it won't be a real game-changer; and that's probably the best you are going to get.
Maybe if Jinteki gets some kind of reasonably efficient ice-tutoring operation, then the situational downsides could be mitigated, but until then, maybe you'd rather just have a few copies of Mind Game, or something else taxing?