I think you’re thinking the two things are mutually exclusive, when really you want to use them together!
An asynchronous Django will let you write AJAX views that are more efficient, and use less CPU time - async doesn’t change how you communicate with the browser.
You may be thinking of WebSockets, rather than async, which I agree would be a difficult tradeoff - but Django is not adding WebSocket support as part of the async work, just support to make normal HTTP run faster and in parallel if you want it.