I find it surprising Miiverse has been slow to get in/out of because it's browser based, and the actual browser is almost instant to use whatever you're doing.
I imagine a lot of the slowness, generally, was down to Nintendo being overly cautious about stability at launch and now they have a few months experience of it being used they can take off the cotton wool and optimize things as you'd expect.
(Having said that, the existing load times have rarely bothered me at all. At least the goddamn shop doesn't insist on updating itself for 10 minutes every time I want to use it. I'm looking at you, PSN.)