I'm in the other camp. I always italicise with quotes ( as distinct from internal thought, which I italicise without quotes).
I think the italics are an important although subtle indicator or reminder that there is no face-to -face interaction — no expressions or body language, which makes it different to normal dialogue.
But in the end, it's a stylistic choice. Do what you want, nothing is "wrong". I'll say it's a common convention to italicise electronic dialogue (phone, radio, intercom ... even telepathy in sci-fi.)
Is that a 3rd person thing?
Not necessarily, because in 1st Person you might have a fully formed thought such as,
I think I'm going to kill him.
Compared to:
He kissed the back of her hand, and I think I'm going to kill him.
But as I said, it's not definitively laid out in CMOS or any other guide — although some offer suggestions. It's a personal stylistic choice, more often than not influenced by what we read, and each to their own. As an editor I see lots of variations that are very confusing for the reader, and for me using italics often provides immediate, visual clarity of what's going on. You can write brilliant prose but modern writing can still benefit from visual prompts — paragraph breaks are an obvious example.
But that's me. There is no right or wrong when it comes to style. Even CMOS is the Chicago Manual of
Style and frequently sits on the fence regarding a lot of things.