We can't think so because musing is a big platform and daily new joining are coming in musing.io and also there website is running smooth and there no maintenance work we see in musing so I don't think that musing should start contest of best answer.
Because people who are joined in musing they will work properly and they all gives ideas to other one because due to musing we are earning a good amount and so that we get steem power and also we increase the reputation score in steemit.
There is no any need to musing to start best contest of the day or a week because musing is a beautiful website which giving upvote on writing the answer of a question only so I think there should not be best contest of the best answer.
The person who are new in this website should get benefited by giving upvotes to their answer then it encourage the new user who had joined
