Has mail changed so that Apple Mail is deciding to make all new email accounts IMAP?

Not sure who your email providers are, but generally it will default to the kind of mail that the mail provider supports. If you're adding the accounts in Mail (not the recommended way), hold down the Option key before going to the 2nd screen and you'll see that the button changes to allow you to override the default setup.

You should be adding the Mail accounts by using System Preferences', Internet Accounts.

You should be adding the Mail accounts by using System Preferences', Internet Accounts.

Correction, that should be: You should be adding the Mail accounts by using System Preferences', "Mail, Contacts & Calendars."

If you want to do it in Mail:

Just make something up that won't work:

Then press "Continue":

Continue, then you'll be able to go back and correct the initial entries.