They would have to be a business relying on Twitter for an important function. A lot of developers are in a difficult position, especially if they decided to use social media sign-ins. They need time to develop an alternative and to allow users to change their login method. But many users won't care and will ultimately just stop using the service. The developer may decide to keep paying as opposed to losing a part of their user base.
Users: I don't want to sign up for a new account on yet another website! I absolutely refuse. Developer: OK I've added social media sign in, but you should really sign up and link your social media account to a website account that I control as a backup. Users: That's OK, this is good enough.
*Twitter Changes API Policy* Developer: You should really change over to a website account now. I can't afford the API bill. Users: No. I'm happy with Twitter sign in. This is your problem not mine. Please change the laws of the universe so they don't inconvenience me. This is all your fault by the way and you're a terrible person. Developer: ....