I would accept without much consideration, simply for the reasons people mentioned above. The only thing that might worry me is the fact that, due to the circumstances of having new music every week, you'd either have to create smaller-scale pieces that are pretty good, or larger-scale pieces that are unrefined and unworked. I'm guessing the composer in this hypothetical would have to go with the smaller-scale pieces. This being a downside, the composer could never actually compose larger, better works without having to be able to compose smaller works to satisfy the weekly requirements. Thus, it would be frustrating to any composer looking to broaden their compositional repertoire. But for only three years, it'd be so worth it.
Also, the weekly constraint might be pretty difficult to a contemporary composer because harmonies today are so much more complex than harmonies from the 18th century, especially when Haydn was under the patronage of Esterhazy. I'm sure any composer worth their salt could manage to work within the time-constraints though.