I’m against that deleted scene since it has unfinished effects. Also, on a personal note, I don’t think it’s needed. Doesn’t really add anything of significants.
Granted … I also like Hal’s approach to removing the caregivers all together since they were unnecessary and kind of distracting.
“Luke wants to go off to an unfindable planet and die off as a hermit … oh, but there are some natives he hangs out with” … can’t really be a hermit when you are surrounded.
Anyway, that’s just my two cents. Regardless of Caregivers or not, the third lesson is an unfinished product that doesn’t really add anything.