Back-up all the files on the Classic mode. Then go into the System Preferences and disable the active classic mode. If the client runs a G3 or G4, use a Mac OS 9 9.2.1 or later disc to install the required OS 9 files needed to activate classic mode.
If the client runs a G5, there will be a disc that came with the Mac called "Additional Software & Apple Hardware Test". Run the "Install additional software" .mpkg and classic will be one of the installed applications.
And, yes, most applications can be removed by just deleting the application from the /Applications folder. Other programs like many Adobe programs also install additional support files that may require additional programs to remove.
Yes, I do think the installing/uninstalling methods are flawed.