From the practical point of view, it might be a problem when everybody advances from 10th to 11th level at once and then everybody wants to pass his own advancement quest before others do. While it might lead to quite interesting negotiation phase, it will be quite bad to be the 6th one and know that you will not advance a level for next 5 sessions (and when you do, some others might be already even on 13th level if they get lucky with xp).
Second point is that it is very videogamish. I will not mention double-U Oh double-U, but it smells a bit like that.
I would suggest something else. Let them get the abilities anyway, but if they complete the quest (and this quest should be already paragon-specific, allowing or even requiring them to use new powers), they get something extra - outside of normal scope of the class. Some specific magic item fitting the paragon path, some special ability/stat bonus outside of normal advancement rules. Still big benefit if they take the pains to complete the quest, but it is not blocking normal advancement. Plus, you can vary reward each time depending on the player and group needs/wishes/performance.
IMHO, paragon paths are underpowered from what we have seen currently. Adding a nice bonus on top of them won't break the game. Gimping them further will only make entire paragon thing pointless (and people will just multiclass to one of the basic classes at 11th, for better abilities and less pain with required 'rites of passage').