So first, we can't delay the audio in SkyView for most radios. We have no idea when they are receiving, so we can't wait. We could with some radios like the Dynon.
However, there are a lot of issues if we did:
1) What do you do if SkyView is saying "Oil" when the radio receives? You just stop? Do you continue with "Pressure" 15 seconds later, or say "Oil" again? Do you wait a few seconds after the transmission stops for you to talk?
2) What if you are listening to ATIS for 2 minutes? No warnings? No AoA? No AP mode change announcements?
3) What if you're at a really busy airport? We've all had those flights where we're 12 miles out from the airport and can't get a word in edgewise to enter the airspace because it's so busy. Do you really want the system to just go quiet?
4) What are critical alerts that should punch through? We already do our best to be quiet and only announce important stuff. I think lots of people would consider Autopilot mode changes to be critical.
So, it could be possible, but the not-so corner cases are a real issue to figure out. I'd imagine a post in the future: Q: Why didn't SkyView warn me I was overheating my engine on climb out? A: There was too much radio traffic.