So let's say you have A (root) -> B -> C -> D
Wouldn't you make one request to fetch A (root comments). Then a second request to fetch B (replies of A), another request to fetch C (replies of B) and then finally another request to fetch D (replies of C)?
And you can't fetch B,C,D in parallel, because you don't know the id's ahead of time to request the child comments.
Just something to think about, obviously doesn't matter until you have deeply nested discussions. But if you look at Reddit (or even HN) that is probably the most common case.
I actually have no idea what the right choice is. I only know how I use these types of sites and I usually go depth first. So I'd start with one thread, read it until I get bored, then continue. Not great for your current architecture, but I could be a weird user.
I had to design comment systems quite a few times, so I'm always curious how other people do it. I don't think there's a perfect solution, always trade offs to be made.
Though most dbs can do efficient recursive queries like this nowadays.