Washington should not be the 51st state because it is a special district. The founders of the country wanted the capital city to be independent of any state. Also, there would be no room on the American flag for another star. It would not make sense to make Washington a state.
Washington D.C. does not need to be made a state, it is very tiny area and it is almost inside a state that is nearby it so it would just be a weird sudden change for everyone involved I feel like. It is it's own little thing and so far that has worked for us.