Not sure why Mueller chose to sign with the Blues, as already mentioned they have strength in depth, so he is going to need to see about 3-4 injuries before he gets to play on the big club.
For the deal he signed I would have expected him to pick a club that would have provided more opportunity to play in the NHL, rather than the AHL. The only reason I can see him signing with the Blues is that he is hoping to get in at least one playoff game and get his name on the cup if they win it all