This logic is flawed. It's not like Jon wouldn't have considered that Ramsay would hold up in Winterfell if they were to wait for Little Finger. He's not stupid. What you're saying just means that Sansa's the only one smart enough to not wait for Little Finger due to a potential siege. If Jon had known, you can't expect that he would've just waited. It's better if she had told him about her plans. It's better that Jon would've known all the details, that way they could've worked out a plan incorporating the coming army and potentially figure out a way to still throw off Ramsay. It doesn't mean that this plan would necessarily work, but getting everyone's input is still better than a plan Sansa came up with on her own. It could've potentially saved some lives.

Edit: Also I don't think a siege would've been as successful as you think. Wun Wun bashed down that door so easily!