The key word in your second point is 'offer'. If they were to protect these keys from being pushed they would have to interfere with your first push and add a line to your .gitignore, which you would then have to remove EVERY TIME... if your a developer I don't know how at this point your not like "eh, actually I don't really feel like doing that in every project, that would be annoying".
I would also argue that allowing newbs to become developers without realizing that they are ignoring private key files inside their git repo is just allowing them to continue on to become developers who are not security conscious. You could of course argue back that having to take .ssh/ out of your .gitignore for every project you do hammers the point home for everyone, and it sure would! I don't believe most of us need that, and if that is your idea of improved UX then please don't ever work with me ;) (I'm j/k about that by the way, tabule looks pretty nice and this is all just my opinion, please don't take it personally. I would welcome an opportunity to work with you... just don't go adding .ssh/ in my .gitignore!! :P)
However, I agree with your point that allowing new devs to keep making this mistake and just shielding them from it is a bad idea. With that in mind, it might be nicer if GitHub checked for .ssh files on commit and showed a warning within the web app, letting you know what you did wrong.
This doesn't dumb down programming. It improves UX for everybody, while also improving security for beginners. Why does GitHub offer to autogenerate a readme file? Because it's convenient. That doesn't dumb down programming for anybody.