I've actually already done an extensive overview of this topic here
On private messaging.
This feature was declined numerous times. StackOverflow is not a social networking tool, and it is not meant to be a forum/chatroom. StackOverflow is fundamentally about questions and answers, and not a portal to being living your life on. Every user has the ability to add personal contact information into their profile if they choose. However, this indicates their willingness to allow random people to contact them, it does not necessarily mean that every user feels the same way.
On preventing users with low accept % from asking.
Every barrier to new users is something we want to get rid of. StackOverflow is about content not points. This means that no matter how frustrating it is to not get the checkmark, the fact that there is a good question, and a strong answer (yours) on the site is a net gain for the site. People already comment on and actively ignore users with a low acceptance rate.
This blog post highlights the purpose of the feature.
On incentive to accept an answer.
The users never need to accept an answer, that is just a bonus. There is already the accept rate to indicate that they should accept, and the 2 pt bump to incentivize it. The main problem is that new users don't necessarily know that they should. Punishing them for failure to do something they don't know how to do is the least user friendly thing you could possibly do. But people also don't want to incentivize it too much because it leads to accepting incorrect answers.
Ultimately, we should just leave it as it. The system is strong enough right now.