It wouldn't be that much of a problem, but I think there's enough room for confusion, that I think people just wouldn't bother with it. For example, while it would be obvious that /tiθ/ is "teeth", something like /bad/ could be "bad" emphasized, or "bod". It wouldn't be that hard to disambiguate, but it is a little extra strain on the reader.

Most of the time, italics aren't actually all that important though, and could easily be replaced with other linguistic features.

Edit, another thing is that the slashes is actually graphemic notation, not phonetic. There's no reason that you have to use something modeled off the IPA there, it's just common to do so. You could use any alphabet.

That would be my wager. In particular, it seems they're talking about the / ... / notation described in the first table here: https://en.wikipedia.org/wiki/International_Phonetic_Alphabe...