I think the more popular YouTubers will probably roll their eyes at requests like that. If you want Let's Players/YouTubers to play your game, I'd recommend looking for someone with a much lower subscriber count, as they'd probably feel happy that someone has reached out to them. You help them, they help you.
I've never asked them, but then again I don't know the etiquette of releasing these days! Do we ask them? Are we allowed to do our own? I've always wanted to do a kind of interview with the game playing. Maybe a stream. I'm thinking out loud.
You can ask however its much better if you release your game and people just make them. It will happen if your games good, there are lots of youtubers looking for indie games to cover.
Eh, i sorta disagree. if your an unknown game designer how are people going to find your games to begin with? even if your part of websites like Gamejolt where lets players flock your still going to have a hell of a time getting anyone to notice you if your games dont have lots of hits to begin with. theres actually a lets play chat section on gamejolt for this exact reason. of coarse people will give you hell for asking, but there will always be those that are like, you know what, yeah ill play your game, and sometimes they end up loving it. you gotta take a chance sometimes yah know? a little bit of criticism is worth it if someone actually does play your game. i actually did this exact thing the other day and had 1 lets play guy play the game and upload it, and numerous others played it and rated it 5 out of 5, so i was pretty happy. the game got a lot more attention than it previously had after that.
[Game design makes my brain feel like its gonna explode.]