In other words they provide plenty of value they are just not able to make a living from it.
Instead they should get more people to stay on their own platform by allowing more content to be created there just like Facebook is.
I brought up Google because time spent on a site doesn't necessarily mean a whole lot more ad revenue. What matters is serving up useful ads that provide value to the user and advertisers. Google is great at that - Twitter isn't because of many reasons you've stated.
So maybe twitter should be trying to improve their ad program to serve better ads. If they can't do that well (no way they could do it as well as Google) then perhaps increasing time users spend on Twitter is their best option.
I only wanted to point out that the solution is not self evident. Just because people are using a service to find content hosted elsewhere does not mean it can't make money. The problem might be that Twitter is bad at finding ads people want to see.
You said that twitter doesnt provide value "because they stare at the feed only to find something that then lives somewhere else."
When you search Google you're finding things that live somewhere else. I'm simply pointing out that you don't need to host the content the user is looking for to provide value.
I'm not saying the companies are the same. I'm not saying Twitter can be successful the same way Google has. I'm agreeing with all your points besides the fact that you need to host content to provide value.