YouTube is not forcing your friends to use YouTube, and neither is the government. Your friends can easily view your video stream on any other service.
So "but my friends won't use Twitch instead", is not really a legitimate reason for us to abandon our belief in private property. Sorry.
If this were true, why isn't it what actually happens? Why is there a single dominant YouTube with majority share rather than dozens of competitors none of which has more than a single digit percentage of the users?
Presumably because YouTube is better? Or maybe just easier?
I'm not an expert. I couldn't tell you.
But what I can tell you is that it's NOT because the government forces everyone to use YouTube. It's not even because YouTube forces everyone to use YouTube.
If someone starts forcibly preventing you from using, say, Twitch, then give me a call. I'll be the first one to agitate for getting that restriction removed. But if you and every one of your friends are free to use whatever you like, and you're choosing to use YouTube. Then there is no real problem to be solved.
What it sounds to me like you're asking for, is for us to effectively confiscate someone else' private property because you kind of like it. Well I'm sorry, but this is not Cuba. That's just not how things work here. Here in the US, the principle of private property is held sacrosanct. It takes a lot more than what you've put forward for us to go confiscate and nationalize someone's property.
There are plenty of video streaming services. Your issue is that you don't want to use the others. That doesn't make YouTube a problem. The problem is that you don't want to use the others. And that's not a problem that the Constitution or the government should solve for you.
But you CAN view live video streams at numerous other places.
This is the difference that's glaringly obvious to everyone else, but somehow seems to escape you. DailyMotion exists. Twitch exists. Vimeo exists. Facebook video exists, and is actually larger than YouTube. (by megabyte stored.) Twitter video exists. Instagram video exists. Snapchat video exists. The list goes on and on.
You have to have a monopoly, to break up a monopoly. YouTube doesn't have a monopoly. You, presumably, just like their property more than Twitch or Instagram video or whatever. So you want to use YouTube.
Fine. I get that.
But that's a 'YOU' problem, not an 'US' problem.
Also, if you view YouTube as merely a video hosting service, you're completely missing the point. It's the second largest search engine on the web.
Sure, all you have to do is get all your viewers to switch from Facebook/YouTube to something else. Which you have no real control over, hence the problem.