When activating the option "Require strangers to verify their email address?" two changes happen. The user who just created the account receives the email containing his/her password and an email containing a verification code. Sending two emails is kind of a double check.
After creating his/her new account the user is not automatically logged in and the password is not printed either. So he/she definitely needs the arbitrary password generated by the portal. So if the user receives the email with the password it is already checked that the email address is valid and working.
The email verification mail is in that case not necessary.
Since this option changes drastically the behaviour of the portal for account creation, the introduction of different options could be reasonable.
"Require strangers to verify their email address on change?" (this would be modified) --> should affect every change of the email address except for the one at account creation.
"Send password per email." (this would be new) --> should send the password to the user instead of printing it after successful account creation.
If both unchecked the standard procedure with printing the password would remain.
If "Send password per email." is checked the user would receive the password per mail and can only login after receiving the mail.
If "Require strangers to verify their email address on change?" every account update including the email address change will require a verification. This should require "Send password per email." implicitly checked and avoid sending an email for verification upon account creation.
This would reduce the effort of a user to create an account or to log in after account creation, respectivly.