Apparently there is a setting for this now. In the Alexa app, go to Settings > Alexa Voice Responses (scroll all the way down) -- you can toggle Brief Mode.
The description for Brief Mode is: In this mode, Alexa speaks less, and for some simple messages plays a short sound instead of a voice response
Saying OK is just as brief as the beep. But in other responses I would prefer brief responses rather than verbose responses. Unfortunately I can't have the OK turned on and brief mode for everything else.
BTW, this isn't available to all customers yet. Like most updates, it will roll out to most customers over the next few days. As far as I know this is a US update for now. I assume other countries will get the same update at a later time.