For TV series I want to keep, I’ll use Tablo Ripper (a third party program - thank you @CycleJ) to copy and convert the Tablo file to my pc where I then manually edit out the commercials. Once the editing is complete I save the file to my NAS Server and use Plex to watch these shows.
If commercials don’t bother you, then you can have Tablo Ripper automatically copy all recordings directly to a storage location for Plex to locate and then use Plex for viewing all of your recordings. There are also other programs like Comskip which will automatically remove commercials and can be used in conjunction with Tablo Ripper.
Plex does have a sort of binge watching feature. It will automatically play the next episode of a series for a couple of hours. After around 6 half hour episodes or 3 one hour episodes you must click play again to restart the binge watching.
So there are options out there, they just aren’t all in one box.