You're trying to quantify what's basically unquantifiable.
All other things considered, if you set the volume high enough, it will mask some street input that might have been useful to you.
And if you're actually following the music, then you are paying it some attention - that much is clear.
But everything else is mostly hearsay, personal opinion and debate.
There are hearing impaired people navigating the streets all the time, w/o being particularly accident prone. Hard to see why a self-inflicted limitation would be categorically different.
A bit unwise perhaps to deliberately chose to play a poorer hand that what would have been available.
There's more than music that can distract you. Maybe you're talking to a riding buddy, Maybe you're trying to pinpoint that squeak your bike has developed. Maybe you're just in awe by the beautiful scenery. Maybe you're real concerned about something going on in your personal life.
It's not like we can forbid people to worry or daydream a little while riding.
Music would perhaps be a more consistent distractor, more dangerous as the time adds up. But I can't see why one minute of music distraction would be categorically different from one minute of conversational distraction.
And there's the basics, like how does our capacity for attention work?
And is it the same for all?
Does the human mind only have one bucket of attention to draw from, or are there several?
If you are of the one-bucket opinion, then listening to music would steal some attention that would otherwise have been available for riding.
But just b/c something is available, doesn't mean that it will be used. Solid numbers of improvement/deterioration would be hard to come by.
I often listen to music while jogging in quiet/low traffic areas. There, I can still get enough detail out of the music w/o having to boost the volume to the point where it'll mask possibly important traffic noise.
Maybe the introduction of electric cars will change that, but right now I don't think music while jogging in quiet areas brings any extra risks worth considering.
I just about never listen to music while riding a bike.
With the wind noise generated, I have to crank the volume up so high to get any enjoyable detail out of the music, that it blanks out a fair bit of traffic noise.
Self, and hearing preservation kicks in, and the music go off.
One exception though. I did use music as an aid for cadence training for a while. I see that as some sort of intermediate stage. Didn't need much detail from the music, just to hear the rhythm. Probably caused some degradation, but not as much as trying to follow the lyrics.
Concentrating on the cadence counter would probably have been just as bad, if not worse.
Jogging in areas with intense traffic is pretty much the same as riding. When ambient noise gets too high, the music is no longer enjoyable. Added risk or not, the music doesn't bring anything, so I turn it off.
OTOH, I have a friend who is a dedicated defender of the one-ear theory. He listens to news radio, but only use one ear bud, in the ear facing away from the the road. I wouldn't think of him as daredevil material , and he's been doing it for years, so it can't be that bad.
I dunno about that. Trying to follow a conversation seems more demanding than listening to music to me. But leaving one ear open would seem to limit the risk of missing out on important traffic noise.
To get back to your question:
It's about ambient noise that isn't information carrying.
With riding, it's wind generated noise that's the main culprit. By the time I've cranked the mp3-player up high enough to get any enjoyment out of the music, it's uncomfortably loud, and I'm deaf to any traffic noise short of horns and harleys.
Not that I'm a likely buyer, but maybe a laminar-flow helmet(time-trial kit?) with integrated ear flaps would sort it out. Or to always ride in a matched tail wind.
With jogging, it's a lot less of a problem, But what remains is probably harder to fix.
I want some of the street hum for situation awareness. But I also need a fairly low ambient noise to enjoy the music.
Maybe one could do some clever filtering, saying that the noises that are pure background are in this frequency/dB range, and the noises that are important are in another freq/dB range. Then you could design a set of active headphones that would block one set and let the other set through. Or an app that does some nifty active cancellation processing. Doppler processing might be able to separate out approaching noises from receding noises. That could be a good start.