Re: Why we must to clean tatami after every class?
Why do you change your underwear daily? You might change it in the morning. You might change it at night. But regardless of the particular time when you change them, you still should do it daily. For all the same reasons as why you clean the mat before/after/whatever.
Regardless of when it is done the mat should be kept as clean as possible. If you want to train more after it has been cleaned, by all means do so. Even better when you're done with your extra bit of training clean where you were training.