they'll have no idea when cleaning would be necessaryI wouldn't be so sure about that - I've seen a lot of office workers who probably don't have any idea how printers work know to take the toner cartridge of a laser printer out and rock it a few times when the printouts start to fade.
To me the biggest annoyance with cleaning (besides the ink waste) is how long it takes, and how difficult it is to do a test pattern print - usually it's a long cycle of "push cleaning button, wait a minute or more, then go back to the computer to fiddle with the disgustingly bloated software to get the test pattern option".
What I'd prefer is a simple pushbutton that starts cleaning the moment you hold it down, and keeps cleaning as long as it's held down. Next to it could be a "print nozzle check" button. Instruct the users to use these when streaks start showing up in the output, and there will probably be far less ink wasted as a result. (There will always be the idiots who lean on the cleaning button until the cartridges empty, but that's a problem of the existing system of fixed-length cleaning cycles too.)