Well, your individual dollars don't buy access to a controlled resource, but people in general contributing certainly does. That streamer would definitely do something else if there was no income coming in. The younger generations seem less tied to the idea that money must always be part of a quid pro quo transaction, and are more willing to throw money into a pool to support things they really like. Sounds like a pretty solid step forward in human cultural values to me.

If the streamer wasn't making money would they continue streaming?

You don't have to tip your waiter at the restaurant. But their salary is fundamentally dependent on you tipping them ~15-20%, so by not tipping them, you are effectively stealing from them. Similarly, not subscribing to people I watch heavily is in effect stealing from them.

To be clear, I don't actually like this model of payment. I'd much rather there be a system that could automatically distribute a pool of money in terms of how much I watched.

You can say the same thing about Patreon, donations, etc.

Sure, you don't have to pay to watch them but its a way of giving back to them. And on platforms like twitch, being subscribed to a channel does things like remove ads and access to emotes that are part of the live interaction if you want to participate in that.

Leaving aside the multi-millionaire streamers, I do think it is commendable to take care of the long-term sustainability of what you like instead of being a free rider.