People search google for "Best washing machine". Google shows them adverts for washing machines, customer buys washing machine.
Where is the intent on twitter? To gossip? I just don't see it.
If someone is about to buy something, they're likely to go to google and search. They're not likely to go to twitter. Google gets them at the crucial point before they buy something.
But what if no one is looking for you? What if you are trying to gain new audiences? There's still plenty of money to be made there. Maybe not Google money, but enough to build a company that's worth tens or perhaps eventually hundreds of billions of dollars. Reputable sources (http://www.forbes.com/sites/roberthof/2013/03/27/report-twit...) have Twitter's estimated revenue to be at $1 Billion next year. And the monetization is just getting started.
That's why nobody advertises on television.
When I watch TV, my intent is to see what antics the Simpsons are up to this week, not to go to Best Buy and trade my cellphone in for a newer version or buy a Coke or go to a movie theater an watch a Seth Rogen movie.
Companies spent $140 billion in advertising on US TV in 2012, up 3% from 2011. TV is about brand and awareness, not direct response.
Twitter may not have direct understanding of intent, but they are pretty good at knowing interest, which is sufficiently correlated with intent to make advertisers happy.
(disclaimer: I don't know twitter and never got into it.)
That's kind of the name of the game. "How can we show people ads in a new way that integrates seamlessly with their experience?"
What if Twitter found a way to do it? Facebook seems to be getting the hang of it with their newsfeed ads.
Imho Google does this pretty well with Adwords (those that you see in the search results).
You can build some amazing tools with the APIs Google and Facebook give you, but Twitter is off-limits unless you're an invited partner, of which there are only a handful (I think.)
They seem a little too content to keep it restricted.
And to at least make my missive vaguely related to your post - surely they'd get a lot of interesting ideas on how to revolutionize advertising if they allowed open experimentation.