We have had the opposite experience, our no dig garden has reduced the damaged caused my mice etc.
We used to loose over 25% of our root crops to voles and mice. First I tried to catch them, but as our war progressed I learnt to kill them, it was a question of veg or no veg. I wasn’t very successful at killing them and they were very good at destroying my crop.
As my garden grew I moved the potatoes out and finally had a real no dig garden, and wonders of wonders almost no voles damage. This was too good to be true so I started asking my neighbours – no change for them.
I know the tunnels are still there and I have come to the conclusion that if I don’t disturb the tunnels they go about their business and leave my veg alone. This is the second season with hardly loss of my root veg, I have been gardening this plot for 8 years. I actually have parsnips (a great favourite of my furry friends) this year.
I did wonder last year if we were just having an exceptionally lucky year but my neighbours continue to have lots of problems (they turn their gardens over each sprint) and I am a very happy gardener!
PS I guess the voles are happier too