Would it be possible for it to be made so that private shows can still be entered manually after the cutoff point like with publics? Or even have an enter all function for private shows? 
It would be so useful for players who bought privates and weren't able to get on in time or forgot until after midnight.

As someone who's life has been hectic and I've missed a ton of  private shows this past month - I don't think this would be a good idea.   I think private shows are supposed to be more effort because you get more points from them.

Wait, you can enter public shows after cutoff for the next day? 

I know this has been brought up many times in the past and it's always been shut down for the exact reason Con just pointed out. It sucks missing out on shows for sure, but it does add more challenge to the game which I enjoy.

Being a seller and buyer of shows, if I accept my shows late, I always offer my buyers refunds or to put the week's payment towards next week. But being a buyer, if life gets busy and I don't enter, then that is just my loss, as the seller usually wont have time to try to find a new buyer for the shows or spots before they run last minute.