I think this is a great idea and I have seen a few people do this. Some modify it and attach a dog crate onto the frame. Others do what you have suggested have have a mesh screen over the top.
I have a couple of options for Alfie when I take him out. I have a small metal cage for him when I take him in the car- e.g to take him to the vets. I use that if we're going to be out for a long time, as it has food and water dishes he can't remove. I often take him with me when I visit my parents, as he absolutely adores my mum and it means he's not left alone. I also have a little camping trolly/cart that the cage fits in, so if I'm taking him somewhere where we'll be moving around (e.g a couple of parrots shows I've visited in the last couple of years) then I can pull the cage around in that.
If I'm just taking him out for a walk then I have a backpack carrier for him which has a single perch in it. It did come with food/water bowls but they are just attached via velcro, so the first thing he does is rip them off and drop them... which means I end up with water running down my back! 🤣
Alfie has the same attitude about harnesses. I do have a harness for him and I did try and start harness training a few times... but he hates his back/wings being touched and the loop to go over his head is so small we never progressed that far with it. I never forced the issue because I'd quite like to retain all my fingers! 😁