As part of an increase in the security measures for our company, we're moving to making sure all password logins (databases, servers, etc), are done through a password prompt and never using stored passwords. The hope here is that if a company laptop were to go missing, we wouldn't need to change all our passwords. 

Is this really enough to assume we wouldn't need to change passwords? Is it not possible to recover passwords from memory or disk when they are typed in interactively?

This is a fallacy on several levels.

First, you can't expect people to remember passwords that are both strong and unique to each service. It's just not gonna happen. Implementing this is just begging to have "passwords.xlsx" pinned to half the users desktops (the other half will use "passwords.docx").

Second, trying to prevent password change is a move in the completely wrong direction. Instead, you should invest in a strategy that makes it painless to change passwords as often as needed or wanted and help users (including admins) manage these passwords in a safe and efficient way.

The reason for that last statement is that if there is one thing certain with passwords, it's that at one point, you will have to change them.  An administrator moves on?  Change all your system passwords.  A manager used the same password for the corporate network as well as his son's football team forum?  Change his password. Found a post-it the payroll admin stuck to his screen?  Change his password.

Use single-sign-on whenever you can, provide a convenient password manager for your users, educate them as much as possible and make it trivially easy to change their passwords. That's the only way to make password usage in an enterprise less risky.
