I don't think rugby should be compulsory at school: any child playing a sport, especially a potentially dangerous one, is more at risk if they are playing reluctantly.
Having said that, I am happy for ds (now 15) to play rugby. He's been playing since he was 5 and has gone through the Age Grade Law Variations, from touch only (none of the clubs up here seem to have tags, so they play touch instead from P1-P3), running with the ball in two hands (no hand-offs), restricted scrums/ scrummaging/line-outs to now at U16 playing pretty much the full version of the game.
He is only 5'5" and very slim so not one of the "big" boys but as he plays scrum half, that's not an issue.
In Scotland all club coaches have to have passed their "Rugby Ready" element (which addresses safety) and all Minis (up to 11/12) coaches have to have completed and passed the UKCC1 accreditation and all the Midis (up to U16) have to have UKCC2 Accreditation. (Don't know the requirements for the Senior Club as I'm not involved with it but I presume they also have to have UKCC2).
Don't know about the schools - ds is at a school that is an SRU funded "School of Rugby" so his (rugby) class got extra rugby for the 1st 2 years of secondary and their coach/PE teacher got extra coaching himself, as well as another coach from one of the clubs himself.
The kids, especially at secondary level, are not supposed to play 2 days in a row - it drives dh and that they get away with it (in fact, he is going to take it up as an official complaint as a change in the Youth set up this season meant that the "top" tiers no longer needed to submit team sheets because they were "trusted"
) - it is the private schools who are mostly at fault here.
Ds' club is "Positive Coaching Scotland" accredited: this means that we don't encourage a "win at all costs" mentality and encourage (to use the jargon) a "mastery culture, not a scoreboard culture".
Safety is taken very seriously: any suspicion of concussion and the child is taken off and after concussion, not allowed to play for 3 weeks. Dh is up at 9 every Sunday and if it's too hard, then the games are called off (although in most cases, they've been called off because they are waterlogged/there is standing water).
Can't remember who it was who suggested protective gear like scrum caps and body armour: I'm not in favour as the evidence suggests that players just feel more invincible and go in harder. (Scrum caps may have a role for those actually in the scrum to stop cauliflower ears). To use the American football analogy - the brain will still rattle in the contact, even of you're wearing a helmet.
Ds also cycles: I watch his races with my heart in my mouth much more than I do watching rugby. Kids can get knocked out in a cycling crash and then are back racing the following day
. Dh did his 1st Aid course for rugby one February a few years ago and had never had to use it for rugby but in the May, ds went to a 3 day series of cycling races and dh had to use his "skills" 5 times in 3 days, just as a spectator - mostly broken collar bones but also concussion. 60-70 kids thundering into corners of narrow paths at 30-40(+) mph means carnage if a wheel touches 
I'm not unaware of the dangers of CTE (which can ultimately cause dementia). I know that a lot of the research has come from Welsh and Irish Rugby, American Football and boxing, because the players' health is being documented. The reason I know this is because my mother died
as a consequence of a head-injury induced dementia following a cycling accident - and her well-documented brain (it took 2 years for her to develop the dementia, during which time we thought she was gradually recovering, and then 2 years to die
) will help contribute to the research as they think there is a chance they can learn to switch off the protein(?) that causes the damage.
But despite this, I still cycle myself and encourage ds to do so.
You can't live life worried about what might happen: you just need to get on with living it.
There is a good blog from the "School of Hard Knocks" - a rugby club set up in London especially for troubled/deprived kids - which talks about how it is the very physicality and potential for injury which teaches both self-discipline and camaraderie in rugby. Can't link to it as I'm on the app and I'm not going to risk losing this very long post 