I don't think YABU because you are making a sound argument and obviously care about doing the best for your DC, so how could you be unreasonable? However I do disagree with you, for all the comments listed above. I wasn't bothered about learning when I was 17 but my parents insisted and I am so, so glad they did.
London is pretty much the only place you could conceivably not drive with no loss to quality of life, and, tbh all of my friends who live in London either own cars, or hire them to travel home/get to weddings/go on holiday etc on a regular basis - i.e whenever they have to leave London!
I live in a big city but would still struggle to get everywhere I wanted to go without driving.
As others said, even in jobs where driving is not necessary, it's still often listed as a positive on job adverts. My current role has 4 staff doing the same job, who started at the same time - 2 that drive and 2 that can't - myself and the other driver have had much more experience offered than the two non-drivers, who moaned that they haven't had the same opportunities, but it's because if something comes in the boss can say - can you get to x location by x time - we can say yes, great, they have to say - oh no, there's no station within 15 miles of there, or there is a bus but it takes 4 hours and 3 changes so the fastest I could get there is two hours too late.
You also have more confidence and more time at 17/18. In addition, even if you pass at 17 and hardly drive (just during uni holidays on occasion) until 22, your insurance would be much less than someone who'd only passed at 22 and need to get insurance straightaway,
You also have the huge advantage of getting to go out with parents (or anyone who has a car and has been driving for 3 years) for extra experience if you are living at home - it is so much faster and easier (and therefore cheaper) to pass if you have 30 paid hours with a driving instructor and 50 practice hours with family member/friend, than having to pay for 60-80 professional sessions. Also gives you practice in driving different cars, which is invaluable.