Though it makes for better TV to have Picard.
If I recall the whole thing was deeply personal and embarrassing, and with Sareks powerful Vulcan emotions escaping his control he was even more stubborn in refusing to admit a problem or that he needed help.
Picard, being an accomplished diplomat himself, was able to convince Sarek he was putting the mission at risk by not accepting help. And he was a good fit for the mind meld both because of his ability and because he was a human. Because let’s face it, most vulcans are judgmental as heck (which probably would have bled through a mind meld)
I’m thinking the Vulcan aids would have more ability being Vulcan and having the mental discipline and training to control their emotions. At that point his aids knew (one was already telepathically propping him up somehow, limited as that is) so not much judgement left.
I think it was straight up pride. Sarek, being Vulcan, wouldn’t really give a shit at a personal level if a human experienced Sareks emotional shame. I love my wife, but I don’t want her in the bathroom while I take a dump. My cat? Meh.
My cat? Meh.
I think this is the biggest part of it. Vulcans are insanely racist. We’ve seen that time and time again.
