Your point about your expectation of being able to like or comment on the post directly on my website is interesting. I took the comment box off of my website a long time ago, with no regrets. I like that it encourages people to write replies in a space of their own. (Ideally on their own website, but at the very least from their own Twitter account).
However, it would be interesting to see what would happen if I let people "like" posts directly on my website, even if they don't have their own website yet. Maybe I'll do that for one of the 100 days!