I hope the monthly challenge will always be around and becomes a feature.
If that's the case then It'd be far more convenient (no DRY), if submit on the problem page also submits to the monthly challenge.
For premium users, autocomple and other features doesn't work on the challenge page.
For not contest users, It'd be a great suprise to receive 10 points and a motivation to participate in the contest. They might just discover about the monthly challenge this way.
And, I think the UX on the problem page is just better.

Please do not make rules that software can easily handle.