Have you thought about how Twitter would actually structure something like that? Twitter is monetizing FAR FAR better than any of these other small Twitter API clients. Something like Tweetdeck might have generated hundreds of thousands of dollars, but thats a joke compared to the kind of money Twitter is dealing with.
I hate ads as much as anyone, but they are working for Twitter. If you think Twitter's executives don't know what they are doing, you underestimate them.
Regarding ads, people consume twitter for opinions, networking and links to content. They are rarely with purchase intent, as opposed to when they are actively searching something on Google, for instance. Facebook are facing a similar problem with their ads, but Facebook still has a much larger userbase and the time spent on the site is much larger than with Twitter. Promoted tweets are too obvious and often have a reverse effect on people who receive it.
The point is, you have no data to back your assertions about what's good for Twitter as a business. They spent years refining their business model based on their data, and they picked the one they have now.