My android garbage phone pauses media if Bluetooth goes away. The only thing that won't is a literal LTE/4g call, that goes to handset.
I was baffled at that comment too. iOS should pause playback on headphone disconnection (wired or otherwise) as well. My only guess would be some sort of rogue app that doesn't respond to OS notifications, so it continues to play sound even after disconnection. In that case the OS would obligingly send the audio stream to the default device (ie. on device speakers). That said the default apps (eg. music or podcasts) should be fine.
This happens most often on calls, since battery life is much worse (60%?) when speaker and mic are being used. That’s why I’m left scrambling to get the other earbud in — someone is talking whether I can hear them or not.
My bigger issue is that my AirPods no longer give a warning when they're getting low on battery. The first time the sound chimes marks 3 seconds until it's about to die. I'm left scrambling to get my other one out as my phone reverts to handset audio (in my pocket).