Using a phone is another way of using multi-factor authentication, and certainly enhances security if done correctly. It is not a substitute for a password or other information, but often times authentication uses both "something you have" and "something you know" concurrently to verify, as it mitigates the possibility that either a) your password is stolen and b) your phone is stolen or hacked.
Stated differently, if you have your phone and someone hacks your password, this can stop them from obtaining unauthorized access. If you have your password but someone steals your phone, this can still stop them from obtaining unauthorized access. Someone would have to have your phone AND know your password to many any major changes, which is an additional safeguard.
While it is a secure method, there are two major drawbacks: 1) the obvious, that if the phone is lost, stolen, replaced, dead, etc, this entire process is moot. If there is no password, there is no workaround. 2) This is a cumbersome process that most users would not want to do. Despite these difficulties, 2FA is becoming more mainstream because it is far more secure than JUST a password or JUST a text.
In terms of security, this is not necessarily "more secure" or "less secure" if you use just one method (phone); they are susceptible to different forms of attack. You might consider it slightly more secure overall, assuming that nothing ever happened to the phone - but that's part of multi-factor authentication. But even so, protecting the phone is still only half of the battle. MitM attacks to receive the text, for instance, are new threats here compared to a password using SSL/HTTPS. Moreover, the random value can potentially be guessed via rainbow attacks.
You'd probably be better off forcing stronger passwords to balance convenience.