I have anxiety, to the point where I’m receiving treatment for it.
I also have 3 children, two just leaving the toddler stage and one at 11. I have always been an anxious parent, waaaay too overprotective with DS1 (he got sepsis at 15 weeks) and in hindsight I held him back, a lot.
I realised when he was about 4 that I wasn’t being fair to him and that my anxiety was just that, it’s mine, and it shouldn’t affect his life or his enjoyment of being a child.
So I get where your DH is coming from, but it’s the anxiety he needs to address not wrapping your child up in cotton wool and preventing them from being a child.
Our back garden is gravel, decking and paving slabs. Beyond padded mats at the bottom of the trampoline ladder (it’s about 3ft on to concrete slabs if they fall) I don’t restrict their running or try and make everything safe. Because kids fall, they skin their knees, bump their heads and graze their elbows in the course of playing.
If you constantly restrict everything they’ll never learn to assess risk for themselves, never learn how to pick themselves up after a minor bump or fall, and most importantly, make them scared of everything.
So aye, I understand his fears but he’s addressing them in the wrong way. It’s the anxiety causing the problem, not your child running.