The seemingly apparent advantage of storing passwords in plain text is that it can be emailed to the user, as the article points out (helps with user retention). This is a bad decision and similar goals can be achieved with better means; the reason it is bad is that the password is then reversible, and hence hackable; and also the password could be sent in plain text across unencrypted protocols.

A much better way to get users back to your site who may have forgotten their password is to have links back to your site that contain special purpose unique tokens that authenticate the user into a minimal state of 'logged in' - a state that allows the user to feel logged in, eg. have visible their username, profile pic and (possibly) unread message count etc. all fields that are not overly sensitive. As soon as the user tries to make a user action such as post a message or view their own private data only then require them to enter their password.

For extra security it could also be a requirement that a cookie identifies the user's browser as being once logged in some time in the past.

This is what ebay does, and probably other sites too. You have to be very careful to make sure it's not going to comprimise any serious security, and is not suitable for all sites (eg. a bad idea for any banking site).