Earlier quoted context omitted.
No. I've implemented precisely that and it doesn't prove what you think. What you do is have one single function create the user, pick a random password, set it in the database (which in my case uses a perfectly sensible hash) and send the user email. The cleartext password in the mail comes from the function's local string variable, not from the database. Whether doing this is a good idea is another question. IMO it…
How often do you purge your mailserver's logs (or if you use a mail API, how often do they purge their logs)? If it's "Never, I didn't think of that." then all your user's inital passwords are sitting there for the taking. Of course, you may have a system that forces a password reset on login. That won't help the users who have never logged in. Those accounts are freely available to a hacker. Plaintext passwords anyw…
The recipients' servers store the message with the password, of course, but they also store the other messages the same user has received from the same server, which in my case contain the same information as what could be accessed with the password. So the password offers very little additional value to an attacker, compared to just reading the mail.