TL;DR: Lemmy and Reddit aren't the "true successors" of the old school forums, but their advantages over forums are considerably bigger than their disadvantages.

Lemmy and Reddit-like systems have a lower barrier of entry and higher discoverability, but forums are more organised.

Pretend for a moment that you had to individually search and sign up for every Lemmy community that you've posted. (If you're a new lemming, sub it with subreddits.) Would've you posted in all of them? Probably not - you'd simply post in a few of them, and forget about the others. That's what killed most old school forums.

And, sure, you might create a big forum about "everything", and then fill it with subforums and sub-subforums about specific themes... except that it'll become an unmanageable mess "behind the curtains", as often moderating a subforum about a certain theme requires some knowledge on it. Lemmy and Reddit don't hit this issue because moderators are mostly independent from the admins.

On the other hand, a good forum will usually encompass all aspects of a certain topic, and it'll be neatly divided into subforums based on focus. Like, a cooking forum split into subforums for recipes, techniques, food safety, etc. In the meantime, a cooking Lemmy community will likely have all of that dumped together, and you'll need to filter out what you don't care about.

It would be possible to implement subforums in a Lemmy-like platform, but that's low pressure. If a subtopic becomes too common in a comm, people create a second comm to talk about it.

I'm not including Kbin into this discussion because it seems to me more like a "bridge" system for Mastodon (microblogging) and Lemmy. Nor Discord - Discord is basically a chat platform, that some people use for forum-like discussion.