Undoubtedly a poor design choice, I appreciate that you bring some attention to it.
Facetime calls are instant. Imagine you clicking a link, your phone calls my (attacker) account, I instantly pick it up and (yes) save all the frames. Now I know how your face looks like and maybe where you are. Hello pretty!
Yes, it works. I tried.
Can you please provide some evidence that this is practically possible? Last time I used Facetime it took quite some time before the connection was established.