one needs to be willing to engage in further discussion when people point out problems with the answers there

I don't really agree. Up to a point, yes, but one reaches that point quickly.

For example, we get theists every once in a while insisting that we engage in further discussion when they point out problems with our reasons for atheism. I often engage them in further discussion, as do others, although I wouldn't say we need to... it's not like theism is some kind of obscure philosophy that we're simply not acquainted with the compelling arguments for.

If we instead got one every few days, I would not engage them, and I would also recommend that others not do so; at that point silent downvotes would be a superior response.

Reasonable people can disagree about where exactly the threshold between those points is best drawn, but I think it's clear that it needs to be drawn somewhere.