Funny, I'm the exact opposite. Most of the chat programs I use (or have used) use the combined approach. Telegram, Facebook Messenger, and so on all have the "buddy list" permanently attached to the conversation window such that you can only see a single conversation at a time. I prefer the MDI of yore since I can have multiple conversations open at once (on desktop, I realize this isn't feasible on mobile).

What chat apps use separate windows? The only one I can think of is Steam.

Pretty much every older chat program used this at some point including Google chat, Yahoo, MSN, AIM, Pidgin, and even Skype.