In my opinion, if steem could be distributed over an indefinite period of time rather than just 7 days on a post, the quality of posts might improve.

You could spend hours and hours writing, editing, and tweaking a post to perfection only to have it earn $2. Then you could post a picture of your breakfast cereal and earn the same $2. Over time, the better quality post would probably continue to earn money where the cereal picture probably would not do as well. With the current payment system, this just isn't the case.

I don't see why a post couldn't have unlimited payout time. It wouldn't change the reward pool, just the amount of posts eligible to draw from it.