Fibbke
If you want lifelong fitness for your kids why don't you get stuck in? Instead of moaning that they have to run a race once a year? Take them to parkrun every Saturday = lifelong love of fitness plus they'll boss sports day next year. Win win.
Or just do fuck all and moan on here about how nasty teachers are!
I do. I'm even a RD at a junior parkrun because I believe in making sports accessible and inclusive to all. I had a really theraputic "snowflaky" moan a number of pages back about some of those moments when I cracked in the face of my relentless sporting ineptitude. So despite dumping the skipping rope on sports day age 7, and flinging the rounders bat at the playground after failing to make it to first post yet again aged 10, I have actually had the resilience to download C25k, and one year later complete my first HM, the last 3 miles in agony and go on to complete many more as well as being a parkrun regular in lycra and hi-vis.
Parkrun gets it right because it's the participation that counts. Competition is entirely personal, be it aiming to be first finisher, chasing pbs or just complete the course. It does of course have the advantage of being voluntary and not in front of a captive audience unlike school sports and sports days which is why they've filled 20 pages up with controversy.
50 times I've been proud of my DCs for getting up and doing jnr pr. Sometimes they get pbs that make me jealous. Sometimes they take it easy. Sometimes it really isn't their week and they drop out. But they come back again and again, so something must be working. It also has the benefit of not being pitched against the same small predictable cohort every time. I can console my DCs that they might not be the fastest, but they have great stamina. Their effort is always acknowledged and that's where OP's HT (and my PE teachers) went so horribly wrong.
There are so many people who are put off exercise long term, either for decades or permanently by insensitive methods of managing sports in school. I was fortunate that I did something out of school and fell in with the DoE Award at secondary. The best way to build resilience is to be stuck in the middle of nowhere knowing you're stuck there until you get yourself to civilisation 
I don't begrudge the winners at all. Just don't showcase them at the expense of those who struggle. Out of 5 school years, my DCs have ratched up "writer of the week" once (It was the first time he wrote about 3 sentences and the words could all be interpreted into English). My DCs have of course noticed this gap in their achievements, but it's not drawn to anyone else's attention, and in a field of awards for numbers of reads, stickers and polite behaviour where they have more control over earning them, it is a less public way that they are affected by their struggles compared to being made to race in public.
Often children who struggle with sport struggle elsewhere, particularly if conditions such as dyspraxia are affecting their gross and fine motor control compromising their letter and number formation. Every part of school life is impacted then.
Because school sport was so horrendous to me, it was important to me to give my DCs a broad, non-competitive sporting life outside school to develop their skills and confidence right from the beginning. It's been a sound investment of effort for DS1 who would otherwise struggle with his dyspraxia. Being unremarkable at sport has taken a lot of effort in the background to get that good. Fortunately his school runs a good sports day with good odds of success.
The best bit of irony was that in my days of casual supply teaching, PE was my most lucrative subject as few female supply teachers would do it Oh if only Mr G could see me now... and it certainly wasn't through any positive inspiration on his part because he was just a foul living cliché of a PE teacher at their most obnoxious. Yup, a mobile phone taught me where he failed for years I have also met many decent PE teachers.