In case of Discord, there are three key causes for preferring the desktop version - and I don't see any easy workaround to them without adding explicit support to web standards:
1) custom audio codecs & filters; Discord is primarily a gaming VC app and the codecs available on the desktop version are superior for purpose of cancelling echo, noise etc. at low latency,
2) ability to capture any keyboard & mouse shortcuts for VC activation
3) ability to use voice & keyboard shortcut while the browser window is not focused (in particular while in game)
Incidentally adding general support for those to general browsers would lead to subtle security bugs & gotchas.