Stuttered video when mirroring from iPhone to AppleTV

Anytime I screen share from iPhone (any model, but including a relatively new iPhone 13) to my any of my multiple AppleTV's (4k model), the video is very stuttered (jerky). Any tips on solving this?

I know the first question that'll be asked is whether my wireless router is fast enough. It should be. It's a modern TP Link Deco that's got Wifi 6.

The core problem seems to be that the iPhone/AppleTV doesn't buffer enough. The video does play. Just not smoothly. As a longtime Apple customer, this feels "broken." But I don't think it's my router's throughput that's the bottleneck. So it's either the iPhone or the AppleTV...