I don't think this is a good idea because it'll inconvenience every single user who posts here, not just the shitposters and bots. Second, I don't think it'll do any good whatsoever toward suppressing....whatever. People here are dedicated to posting shit and won't let a silly little captcha stand in their way.
That's the whole idea of it, if they really want to post and if they think the post that they want to share is something that can help others in the topic of discussion, just like what you said no silly little captcha will stop them for posting, but for a bot to solve a captcha for every post? If that idea will not stop them from posting at least it will slow them down until they are identified as a bot then ban.