It's not a quest, exactly -- or at least not in the same way. You can enter the initial room in one of a few ways, I usually take the door that's behind you when you are looking at the posting board where you read about pvp quests. Then you get teleported to the room where you see a portly guy and a lynn who you talk to to say what floor you want to go to. I suppose you could look at that as the start of the quest sequence. However its not really automatic, they've just hidden the taking/start of the quest into you telling the lynn what floor you want to goto. That's the point -- this game doesn't seem to have much in the way of auto-repeat quests. It has quests that start when you activate some "trigger", like talking to someone or killing someone or entering an area. But in all of those cases, it involves you taking some action. For a quest like gathering kills, in that area, the kills can go toward 1 or 2 quests at the same time -- one is the daily, and one is the repeatable, but AFAIK, all quests that you can repeat have to have some start and stop point so it can flag beginning and end.
While it would be convenient to have the quest "renewed" automatically, that would effectively give you "loot" for simply walking through an area and killing enemies -- like automatically giving you something with every enemy killed. But the game already does something like that in that it gives you money and experience for enemies killed. AFAIK, that's the only quest that you don't have to enter or exit and that has no defined start/stop points, but that was sorta what I was getting at. All of the quests, as they are currently laid out and defined have to have some start and stop point and have to be for actually doing something (vs. rewarded for things you you have already done). So it would, at least, be inconsistent with other quests to automatically give rewards for kills where you haven't taken or activated or started some specific quest.
Certainly they could make the UI more user-friendly, but as I mentioned above, that would be inconsistent with current design.
The UI is sorta like the original design or layout of the keys on a typewriter or keyboard (the standard QWERTY arrangement). IBM went with that design because it WAS difficult and was deliberately designed to *DE*optimize typing speed. They tried several designs, but when they first designed it, it was done with not-very-reliable mechanical parts that could easily jam. They found that if they optimized things, people would type too fast and the keys would be more likely to jam. So it the original design (that we still used today) was done because it was a bad design that slowed people down. If the BnS UI was optimized, people could likely do alot of these time-consuming and tedious tasks in 2 or 3 times the speed -- but that would allow people to progress to fast, too easily. Thus the design is created to slow down progression and how fast you can go through the game. Unfortunately, such anti-player techniques usually influence a players overall perception of the product, negatively and reduce the 'fun' level and cause people to give up playing it more quickly. Thus the game's popularity falls off soon than it might otherwise.
Game manufacturers can't disrespect users and not expect it to have some effect. Only in a constrained or limited market where players don't have other options can such techniques be used where the benefits might outweigh the deficits.
Indeed, that could be a major flaw in the overall game strategy by a game manufacturer that started in area with a limited or constrained market -- if they introduce it into an area without the same constraints, they might find such decisions more heavily affect market share and player satisfaction.
There, as I sorta hinted at -- that quest benefits by the fact that you are going in a loop, up the tower, then back down at end, then go by the lynn to specify which floor and you start again.
That's why I said you get used to pressing 'j' right after finishing -- most people do, but I got chided for presuming that most people would be able to, so ya never know .