I suspect this has more to do with hardware limitations on the 3DS. the browser and Miiverse are, i'd say it's safe to assume, the two most demanding things you can do while the 3ds software is suspended.
It is possible that in order to ensure that the game runs smoothly, Sakurai and his team had to disable the use of the browser and miiverse on the standard 3DS so they would have the extra power needed to run those tasks.