Currently, the Weekly Topic Challenge starts and ends on Wednesdays (usually). It seems to make more sense to have it from Sunday to Sunday, especially since each is titled "Weekly Topic Challenge ....(week of [Parsha])".
The current timing feels a little "off" to me (I think I've posted "weekly topic" questions on Thursday, when it was technically late, twice now), but I think the "think about it over Shabbat" angle is important too. Would Friday to Friday be a better fit? (Then it would be the "week of" the following parsha, the one we read at mincha the day after the topic is announced.)
The benefit of Wednesday, as Isaac Moses notes in a comment, is that it gives people a chance to see the topic before Shabas so that they can think about it over Shabas, even if the new topic gets posted a day late, on Thursday. That benefit is pretty much lost if the day is moved.
I'm not sure that that benefit outweighs the benefit of starting Sunday so the topic matches the calendar (and parasha) week, but I'm inclined to say it does.