Each step of a quest can have its own requirements. There are level requirements, class/job requirements, prerequisite quest requirements, items available in inventory requirements, equipped gear requirements, and probably others I can't think of offhand. Any of these can be set separately at each step along the way towards completing a quest, and it's not unusual for at least some of those to be different for the turn-in step than they are for the initial accept step.
That doesn't explain why on some quests SE seems to have entirely left out one of the major steps, namely the step where you accept the quest. On most quests, the level requirement for accepting the quest is set to the same level that's used as the level requirement for turning it in. On these ones it's not.
If the level requirements were consistently just one level lower to accept than to turn in, I might believe that, but on these particular quests, there doesn't seem to be a level requirement to accept it. A simple kill three mobs and come back sidequest isn't going to gain you multiple levels, and some of these don't even have that much. Some can be accepted at level 1, have no XP generating intermediate steps, and can't be turned in until level 17 or 18. That doesn't look like a deliberate rule allowing for level progression while completing it. It looks more like a bug or just plain lazy implementation, where the level requirement just never got added to the initial accepting step of the quest.
Yes, but not only does it clutter your quest log and quest tracker in the meantime, but it also breaks up the story that way, especially if it takes a long time before leveling far enough to turn it in. You end up being thanked for something when you may not even remember what it is that you did to be thanked for. And if there's really a conclusion to the story (beyond simple thanks) when you turn it in, that disconnect is even worse.
That accounts for having a level requirement for turning in a quest, and I haven't seen anyone argue against that. The problem isn't the requirement on turning it in, it's the lack of that same requirement on accepting it in the first place.