The thing I hate is the opposite. When I'm told off for not replying to a message. Ergo need to keep it in visual range and stop what I'm doing on each message. Even if it's an inane broadcast from a team member.
With chat everybody has the same persistent view. Email everybody organizes differently.
Some people delete emails after reading them, some put in folders, some tag everything, some have an inbox with 100000 unread emails. If I tell a colleague that I emailed them the info a week ago half of them will not find it and just ask me to send it again.
With chat I can just say "it was posted in the QA chat room about 2 weeks ago" and everybody will find the info equally easy.
Except organized differently, and easier to author rich content with. And the performance is better, messages are sent instantly. The overall UI is better in many ways.
That said email having subjects makes it different.
Until I encounter a problem, switch into chat, and find that someone else already solved that problem and it was archived by the chat system.
Flow maintained.
My chat apps run on a separate monitor that is purposefully not within my visual range of the monitors used when I'm coding.