Short answer: this is by design and unlikely to change. These aren't discussion sites, and the goal of displaying any comments initially is to highlight important information added by a third-party, not provide a lead-in to some tangential discussion.
Details: Comments are - at best - second-class citizens on SE sites. The primary goal is to generate a repository of good questions and helpful answers, not lengthy back-and-forth discussions. That said, there's often a need for users to ask questions, denote problems, or add errata... When comments were first added, they were initially hidden - you got an indication that there were comments, but had to click through to view them. But it turned out, some of these comments were valuable to casual readers as well as post-authors:
There are often important clarifications and addendums left as comments that substantially improve the original post. It seemed a shame that these sort of comments were all locked behind the “expand comments” button, and every reader had to click on that link (or know they should click on it) to get the benefit of those comments. Information was being lost!
So this was the compromise: don't clutter up the page by showing all comments, but pick the best 5 (by votes) or the first 5 (if there aren't any votes) and show them, based on the assumption that if there's any value to be had, it'll be in those top-5.
Again, promoting lengthy discussions as an end-result wasn't the point. Arguably, most readers only care about the end result of such discussions - either as edits to the post itself, or failing that a collection of insightful comments.