The issue with this is the increasing number of people on mobile devices and variety of device types.

Worst case (and sadly most common one): You share the dropbox link, the recipient clicks on it, it opens the browser, triggers a download, he has to choose a download location, download vanishes or takes a few seconds that are spent doing something else, worst case: the person forgets about the file / best case: he digs ups a file manager, navigates to the downloaded file and opens it, player selection...maybe...and all that for a 5-15s just audio-greeting message :/

It should just work out of the box.

People seem to use Messengers for that. Like Whatsapp, which play back recorded or attached Audio. But yet this is only mobile.