There are two problems here, one is reddit preventing new comments on old posts, which is not inherehent to tree-style threads.
The other is that trees make it harder to keep up with ongoing discussions as you can no logner just continue reading from where the thread was at when you last visited. Reddit actually has an OK solution for that which highlights new comments since your last visit(s) but it is only available to moderators or paid users.
Another possible solution would be a better notification system - with forums you can typically watch a thread to get notifications for any posts but with Reddit you only get notfications for direct comments to your post/comment.
The other is that trees make it harder to keep up with ongoing discussions as you can no logner just continue reading from where the thread was at when you last visited. Reddit actually has an OK solution for that which highlights new comments since your last visit(s) but it is only available to moderators or paid users.
Another possible solution would be a better notification system - with forums you can typically watch a thread to get notifications for any posts but with Reddit you only get notfications for direct comments to your post/comment.