Many reasons, one of the more important ones being there is a $100 000 maximum annual income limit with the free version. Make more then that, and you have to buy pro. Also, since its the same download for both free and pro, having you log in is their way of telling whether you should have access to pro features or not.
There are other things, like access to the asset store, though you could argue that it should only require you to log in if you actually try to access it.
It's also a convenience feature. By having you log in, it can figure out all the licenses you have access too. Buy a new license for android? No problem, just restart Unity, and it will be there.