It's a better story. It conforms to the way things happen in Game of Thrones. It conforms to the characters. It was in the end, the better strategy. Bolton's were defeated because they came to the battlefield instead of withstanding a siege. They came to the battlefield because Ramsay Bolton 'knew' that his army will defeat Jon Snow's. They were beaten because they were taken by surprise when Baelish arrived.
As to why Sansa didn't tell Jon, it was simply because of the way she is, this is the kind of person she has become. After years in king's landing, and everything she has undergone with her marriages with Tyrion (yes it was horrible for her) and Ramsay, one thing she has learnt is that she won't under any circumstances let anyone else control her life anymore.
"I'm not going there back alive.". She won't tell anyone anything unless it serves a purpose for her.
Sansa is no longer the naive girl who wanted to be a queen and to have little price and pricesses. She has seen it all, been through it all. She is a survivor. She knew that Jon won't be able to beat Ramsay. Jon fights with honor.
"Ramsay is the one who lays traps.". She also knew that to beat someone like him, she needs someone like Peter. She wants Ramsay dead and she is willing to use Jon's entire army as bait to draw him out.
"Sleep well", she says after telling Ramsay he is going to die the next day.
She also knows her brother is not going to survive this battle and accepts it with steely pragmatism. Sansa has in fact become, a lot like Peter Baelish.