You can use studies for and against so take it all with a pinch of salt I guess. David Wilson’s seminal work Bicycling Science demonstrate that a deceleration of 0.5g is the maximum that a seated rider can risk before he goes over the handlebars. Wilson’s calculated 0.5g yields 6.5 metres with the front brake and 12 metres without it at 20mph. The highway code only demands a 12 meter stopping distance for cars going at 20mph.
But in situations where sudden braking is implemented braking consistently goes past the safe threshold of 0.5g and poses a serious danger to the cyclist of falling forwards off the bike.
First thing, the highway code doesn't "demand" any stopping distance. I advises readers on safe minimum stopping distance in order to encourage best practice in deceleration and stopping their vehicle.
Secondly, just calling something "seminal" doesn't make it the best source of information on the subject.
Here's something, which I concede is anecdotal, but I think bears some relevance. I was out cycling yesterday and at one point I was descending a long steep hill Roadsigns suggest a gradient of 13%. My Garmin put my speed at around 40mph. A car pulls out of a junction into the road ahead of me. To avoid hitting the car, I brake as hard as I can. Not just brake hard but physically cannot put anymore effort into the brake levers. The deceleration is distinct and palpable and I've very quickly slowed to less than 10mph.
Whilst this all happened very quickly and in a state of panic, there is one thing that I remember clearly. During these moments of hard braking, on a gradient that already reduces my centre of gravity, not once does my rear wheel leave the ground. It did lock up at the end but it didn't leave the ground.
So either that 0.5g doesn't carry the implied level of risk of going of going over the handlebars or the consistency and/or frequency of achieving that level of g is not as high as implied. Because of all of the hard braking that I've ever had to do, yesterday's instance is certainly one of the hardest. In fact in best memory, all of the times when my rear wheel has left the ground unintentionally, it's been because I have compromised the centre of gravity of myself and the bike through poor riding technique.
And again, anecdotally, your fear of flying over the handlebars from heavy braking is largely unfounded on the grounds that this is a notably rare event on the road.
As for the consequences of riding brakeless. Well, aside from an increased risk to public safety, you risk a criminal conviction. Sure you may just get a spot fine. However, an accumulation of these may result in an additional charges being pursued against you as failure to rectify an illegal absence of a second braking mechanism could be seen to constituted continuation of offence. Alternatively, in the first instance, the officer and force may decide your actions merit action more serious than a spot fine and you may be charged with an offence resulting in a criminal conviction. That in turn could have an impact on your future employment prospects, access to credit and financial services and many other things besides. Not only that but, should you be involved in a collision then you are making yourself vulnerable to civil litigation regardless of whether you would otherwise have been considered at fault. Any insurance that you do hold to protect you against this may be considered invalid for failure to observe the law regarding the the roadworthiness of your bicycle.
My advice, go ahead and ride brakeless. It's always really funny to watch someone's life get fucked up because of their own actions. These are hard times, the more lols the better.