That's a good question. I don't know -- I never considered private browsing. If I close a private browsing session, are all traces (ie: cookies, history, etc.) of it erased? If so, I don't think that's what I want. I'm okay with my bank (and websites I trust) setting cookies, for example.
Yeah, private browsing / private session / incognito mode will stop you from storing cookies and session data.
Sure, but my bank and (like most other highly trusted sites) doesn’t set any useful cookies anyway. I think there is an option to autofill my username, but why bother if my password manager does that anyway?
If I open something in private browsing, that’s a time where I especially want every bit of BS blocked.