Right on your first point.
Part of the reason why assassins aren't played as much (in general) is that supports make it nigh impossible to actually kill the ADC. Throw in the tank top or jungle with their own locket or knight's vow, that carry isn't dropping anytime soon.
But the other reason is that mages waveclear too easily. The way assassins are supposed to work is that they push a wave out, then use their superior mobility to gank another lane. The problem is is that now they can't roam into other lanes, because the time difference between mages shoving in and assassins shoving in is massively in the mages advantage. So the mage just waveclears out and pushes to the tower, which means the assassin can't leave lane without losing a large chunk of their tower.