Kase-san should know how Yamada is and can't say no easily because she's a shy girl.
She should have a little more faith in Yamada after all this time.
No, she shouldn't, as you said yourself:
Kase-san should know how Yamada is and can't say no easily because she's a shy girl. >
Yamada clearly had no idea what she was doing from the beginning and the speed at which she lost control of the situation just show that Kase has no reason to trust her when it comes to dealing with men and strangers in general, as someone else already said, you don't throw someone who can't swim into the ocean.
Kase reaction was right and completely justified in this situation, Yamada wanted to show her that she was a big girl and almost got burned, in the best case scenario she would have had a very unpleasant time, and in real life (or in a much darker manga) it would have been much worse than simply unpleasant.
If Yamada wants to learn to become more independent there are much safer way to do it, but it wasn't just about becoming more independent in this case, she also did it to spite Kase, to tell her "I don't need you, I can do whatever I want" and it was an absolute failure.
On an unrelated note, what's up with this whole mixer culture in Japan? Does this exist in other country as well? There is no such thing in my country, and quite frankly, it seems completely stupid to me.