The concept of the game is "keep playing a level without having to abandon it".

The concept of quests is "play until you finish quest, then restart level to get the next one".

This is annoying and time consuming, in real-time terms.

Is it possible to load a new quest as soon as one is finished?

Multiple quest slots still help since you can do them concurrently, but it will not be as irritating to farm quests when all the levels are already completed.