Honestly, just asking a big person to collab is silly in itself. Do you realize how many times a day they get asked that same question over and over? No one feels like being used all the time.
Just gain subscribers promoting yourself and putting in hard work. If a big youtube gave a shoutout to every person, it would become ineffective. People want to see household names like DailyGrace, Joey Graceffa, Connor Franta, they don't want to constantly see these fresh faces, there's just no interest in it for the audience that popular YouTubers have.
and honestly, ONE shoutout will hardly do anything. You may gain a few thousand subscribers, but in the game of YouTube 1000-2000 subs is basically nothing. I've seen channels with 2000-3000 subs that are still basically dead with loads of likes, and barely any comments.
I used to be able pull 1,000 views on each of my videos with 700 subs on my old channel back in 2011, now people with 3,000 subs can barely get 500-600 views on their videos. Times are different, and conversion is tough.
The only way that a shoutout from a top tier YouTuber would be helpful is if they kept consistently promoting your channel, and obviously that's not going to happen.