It's not only the launch that takes so much time,but nearly everything,Microsoft account/skins/marketplace/loading a world/opening a chest.But i found out that the game shows time to time "loading ressources packs" but i've got nothing beside the mario one (not even active).You can maybe also try calling nintendo,it's their console so they might know something about a storage difficulty...
The game also crash at the menu,when loading a solo world or randomly when playing it,and this could due to the same problem since in a second account everything run smoothly
One way to resolve the problem is to go to the home menu if the console is too noisy and continuing the lauch preparation when it becomes quiet again.Also go to airplane mode and things will go faster
Its a part of the update,the good discount was apparently a bug
Even if the issue is fixed,it may come back like last year...