What makes them feel like 1970s technology: everyone has to manually manage their own archive and pay storage costs for media files, there is no way to share history (if you want), there is no integrated search, differences in clients mean that people have different experiences of the same message, there are no affordances like reactions that allow people to easily interact with a message without sending an entire separate message.

But maybe I should have said late 80s, early 90s tech. In the 70s, if you were communicating with others on a computer, you were almost certainly using the exact same software on the exact same time-shared system, where at least there was a symmetry of experiences (but no multimedia). The explosion of email clients happened in the 90s, mostly.