Another one born and raised in SE London here. Absolutely yes to the best of both worlds; on the edge of Kent, short drive from Sussex, open spaces within a short walk away, and could access Central London within half an hour.
This said this was the days when a Red Rover ticket allowed you to roam the city all day without a mobile phone, though I do remember being given a phone card for emergencies.... I doubt I would be allowing our child to do the same at such a young age but it was great for me, we are though in different times now, so I expect this caution would apply anywhere ?
Visited bundles of museums and galleries and am now beginning the same full circle with my child.
I definitely think London perhaps makes you grow up a lot quicker and a lot more streetwise, this was very evident amongst my peers at university and even now amongst adult friends who still sometimes appear more than a bit naive and less confident in themselves.
We have had the same conversations as you OP, but the positives and possibilities here far outweighed the negatives when we really considered it. I do worry that in teenage years children here perhaps have access to easily to somethings they shouldn't , but hoping to navigate that one with a close eye and lots of guidance.
So for us, we have the luxury of having the ability to escape to the countryside on a whim, have parks here in walking distance with nature reserves on our doorstep, but also benefit from the buzz and opportunities we viewed to be unmatched anywhere else.
OP I hope you choose whatever is best for you and yours . It's a tough call these days and I think only you know what works for you.