Delay between audio and video when using Bluetooth headphones. All apps, and various different types of hardware. What's the problem with iOS?

I doubt that it is a problem with iOS, because if it was you would see millions of posts about it (there are 800 million iPhones in use). So it's best to start troubleshooting on your own. First, a reset is a good idea - hold the HOME and SLEEP buttons until an Apple logo appears (about 10 seconds). You won't lose any data.

likely it would act the same connected to a computer

there is nothing in the a2dp bluetooth profile which send back feedback about

progress, so if the audio headset spend time on clearing up the audio quality

or if it's component are just not able to do it fast what you experience happens

it's pretty widely known for all wireless headsets