Should I postpone my MEXT scholarship application process until 2021 due coronavirus outbreak?
At this point there are no guarantees. Things could be fine in a year or not. There could be a vaccine or not. Japan could be doing well or not. The pool of applicants could be stronger then or not. Travel may be easier or not. There are just too many variables. 

Under the circumstances you are probably best advised to continue on with an application until you reach a firm decision point (acceptance, say). Perhaps more will be known then. But expect chaos in the near term. Too many governments are behaving incompetently and making bad decisions. That could change or not.