The way of setting the password on registration with the wp-system is troublesome. The same with "Forgot password?" procedure. It all depends on the rigid means of the WP system. Dry, minimal email texts. Login form from the last century. And at the end the customer logs in right there and enters the land of the backend - and feeling lost!
With a secure direct login link in the customer notification email to access "My Appointments" this is all history! This is the way to go today. This is what customers enjoy and feel welcomed. No more fumbling around clicking to receive an email, there clicking again, then entering your name and password to register, and doing the same thing all over again to log in, only to likely end up in the backend!
Don't you think?
I solved this problem by installing 4 (!) plugins to work around it! (php-code didn't work out in the time I had, to tricky for me. For others as well, by the way).