It's not that the bikes aren't suitable - we have seven, two of which are proper "look mum, I can ride down cliffs" mountain bikes.
It's more the overall experience, everything being coated in mud, the mud itself being coated in mud, the chain being barely visible through the mud, your cables gum up, etc. etc. (mud is not the worst thing on the path either, but how can you tell in advance?)
And then, covered in all this mud despite your SKS full mudguards, you get to the supermarket and you have to walk around and do your shop, then get it back up the hill, without breaking anything or covering it in mud.
All in all, I'm not that upset about driving there per se. It's ten minutes each way as we don't shop in rush hour.
I just find it interesting that there is dedicated, fully segregated cycling infrastructure between my house and the second most common place we go, we're both very active cyclists, and we drive.
I'm sure people think of it as valuable infrastructure and I'm sure it's included in all the counts of dedicated cycleway km etc., but I wouldn't object to a bit of tarmac :)