Could just be security based. Sharing accounts is bannable, so to prevent accidental bans, and to prevent lets say, Your little brother or sister from logging onto your account, you have to type in your password.
How mad would you be if you had a sibling that decided to goof around on your computers games, and it auto logs them into league and they go play a match not knowing a single thing about the game? And then maybe even possibly get your account banned for "trolling" or "intentionally feeding" when in reality they just didn't know what they were doing xD.
I imagine it's really just a security precaution, most accounts have a credit card number saved as well, so it could also be to help prevent unwanted purchases that you yourself didn't authorize.