Maybe it would be interesting to have 'Picture of the day'. The theme shoud be free for this. 'Picture of the week' could remain the same, or it could be the best picture from that week from 'picture of the day' themes.
Let's not do that.
The reason for "Picture of the week" contest is only to find a suitable photo for the main page header. It is not a primary feature, and certainly not absolutely necessary, but it's a nice way of keeping the look fresh using some best on-topic works of community. The idea was never to be a contest site, so we shouldn't have more of them. And that's also why the contest should stay in meta - it's not the kind of content users should come to Photography SE for.
Based on experiences with weekly contest, I'd say 24 hours is simply a too short timeframe. Sometimes, the weekly contest will get its first entry on second or third day. So, "Picture of the day" would be "the only picture of the day". And certainly, there wouldn't be enough time to vote for the entries. Even if you visit the site daily, the pictures that get uploaded after your visit you won't have chance voting for. Upload too late, and only few will see it competing. No competitors, no votes - that's a shabby contest.