I didn't have time to check spell usage because I'm doing coursework but yeah, there's no reason to not use another spell the millisecond that the GCD finishes. Really if he's going more than half a second wait each time, he may think that's fast (it's not) but now imagine how much it adds up when your fight is 600 seconds long. You're only getting 2 thirds of what you should be.
Find out if he's a clicker, watch if he keyboard turns, and make him read this guide because you telling him what to do, whilst admirable and definitely helpful, he might not understand things (he'll say he does) and you'll have to repeat this every month or so and it'll piss both you and him off. Make him do his own research, even if you have to send him the links, that's still fine. And don't you dare let him read Noxxic, it's not as bad as it used to be but myself and others still have a phobia of that place.