It is incorrect to say Twitter killed its platform — so many companies are and still are built on top of twitter data and information and Hootsuite itself is worth $1B+.
In addition it was critical for Twitter to have its own core apps across all of the mobile platforms independent of whether other apps existed. They even bought a platform app or two which is a nice reward for some developers. The reaction from other developers that Twitter was going to offer first party clients was overwrought and unrealistic.
That said, looking back it does seem silly that Twitter told developers to stop building client apps and restricted them to limited numbers of users.
Instead, twitter could have monetized by running its ads in the timelines regardless of which client app was used, and shut off any client apps that directly removed ads. And perhaps if client apps added careful ad tracking (in the same way first party twitter clients do), maybe twitter could even have given a rev share to the third parties.
Even had a crazier idea at one point to push the ads via retweets so that developers could make no changes and the ads would appear in the timelines of users. Imagine a world where you could see every single ad in the twitter system based on the one account that retweeted ads. Talk about openness and transparency! (No other platform lets you see all the ads, and lots of ad fraud exists)