One of the obstacles is that it would allow users to vote many times on the same post with the same Steem Power.
Currently there is a seven day payout system which meshes with the seven day delay on returning delegated SP. If payouts were set for longer periods, or repeating periods, then it would be possible to use delegation to upvote a post many times using the same SP.
This could be achieved by delegating the SP to a new account each week. The new account would then be free to upvote a large number of the author's old posts before returning the SP to the user (with a seven day delay), with the process repeating on a weekly basis.
This reduces the "proof of brain" required to earn new SP.
(As a note, I believe that the old system with a longer payout period operated prior to the development of the delegation system).
It wouldn't be hard to change, as it has already been done so in the past. When I first got on STEEM, the payouts were originally done 24 hours after posting, and a second time 30 days after posting, but that has changed to 7 days now. It would require a hardfork though because of how big of a change it is and so 17 of the top 20 witnesses will need to agree to it.
So to simply answer your questions, its possible, but would require a large majority of the witnesses to accept the change.
It's actually very easy, as long as the community wants it. What you need is for someone to submit a hardfork proposal of the change, then the witnesses can vote on whether or not to accept the change. At least 17 of the 20 witnesses need to accept it in order for it to become active.
The question now is why? We have tried 24h + 30 days payout in the past, which was the changed to 7 days to make it easier and more understandable for everyone. I personally don't see a reason to change it, but feel free to let me know why you would like it differently.