Virtually all forums (and their ancestral mailing lists) default to chronological order. A good comparison is perhaps the difference between comment-driven and discussion-driven sites, if there's a technical name for that?
HackerNews is comment driven, but does a decent job of facilitating discussions - but not particularly deeply. Reddit is similar. Forums are much more amenable to linear, deep, discussion between a few parties, but can also facilitate comments. Both have their place on the internet, and I don't think that forums are necessarily the answer to everything, but it feels like a lot of people left those communities to end up in Reddit and that's a shame.
Interestingly, old forums rarely supported nested threading. The only "threads" were just linear sequences of posts in a topic. Nested threading is nice but it's also a different cognitive experience that maybe has some downsides as well.
If you reply to an earlier one, the UI will handle it and show a new branch where that conversation started. I'm not a huge fan of typical mailing list web UX and usually view flat, but it's so common that I guess a lot of people like it. My opinion is probably biased from years of using/running forums, so I'm much more used to that UI.
I think newer systems like Discourse will formally track replies to you (versus a new message in the overall thread), while legacy forums like PHPBB usually just quote-reply.
Nested threading for long-running threads only really makes sense when you can manage the “read” status per post (as in Usenet and mailing lists). Otherwise, new “leaves” or subthreads in the thread tree are all over the place, and you don’t know which you’ve already seen/read and which you haven’t. Web forums generally only track a single “water mark” per thread for how far you’ve already read, which more or less implies that only chronological order makes sense. You still have hyperlinked indications of which post is replying to which other post, via quotes.
HackerNews is comment driven, but does a decent job of facilitating discussions - but not particularly deeply. Reddit is similar. Forums are much more amenable to linear, deep, discussion between a few parties, but can also facilitate comments. Both have their place on the internet, and I don't think that forums are necessarily the answer to everything, but it feels like a lot of people left those communities to end up in Reddit and that's a shame.