There's a lot of people over-reacting to this situation.
If you read Twitter's blog post its clear that they're following up on enforcing the API "Rules of the Road" they've had for over a year. https://dev.twitter.com/blog/delivering-consistent-twitter-e...
Section !.5. clearly lays out the rules clients must follow "Your Service may be an application or client that provides major components of a Twitter-like end user experience (a "Client"). An example of a Client is a downloadable application that displays user timelines and allows users to create and search for tweets. If so, certain additional terms apply, including:"
These rules are actually pretty generous and plainly lay out their expectations for third party applications. It's unclear what led to Tweets being removed from LinkedIn, my guess would be that Twitter attempted to enforce their branding rules, LinkedIn declined and instead said they would remove the Tweets from being displayed entirely. It doesn't sound like Twitter just cut off access to LinkedIn or came up with new restrictions they haven't already been publishing (and compelling 3rd parties to comply with) for a long time.
Any business must deal with existential threats, be it from competitors, regulation or bad investments. Building a business on top of an API is just another potential risk, you need to decide if they company in question is a safe enough bet to play on, just like you have to decide the same thing for all other risks.
It was poor judgement and poor PR to lob that out there before they were ready to actually spell out what these new "stricter guidelines" are. It creates fear, uncertainty and doubt among Twitter API developers and they are getting sick of fear, uncertainty and doubt, its been going on for a long time now.
Twitter's message bus, API and identity system have become valuable Internet resources. But Twitter has never been particularly great at thinking of innovative uses for it or developing great clients. There are a lot of really interesting and different ways to use those, regrettably they are trying to kill most of them and inflict a homogonized, boring, monoculture on their user base they can monotize, which will make the experience progressively worse.
At this point I imagine most API developers are wishing there was a new message bus they could move to but its a daunting challenge to field one, even more daunting to get a critical mass of messages moved over to it to make it interesting, and really daunting to fund it without resorting to all the lameness Twitter is now knee deep in.