What I see on the original poster's horse is high heels (notice the frogs come nowhere near to touching the ground when viewed from behind). Clinches that were never cut to a proper length (which, in my opinion, is very shoddy workmanship) and maybe the biggest thing that jumps out and grabs me (which has nothing to do with the farrier) is the growth rings in the feet. That can be a sign of low-grade laminitis. So that might be something to look into, especially if the horse is on grass or getting grain. You can have the best farrier or trimmer in the world, but if you have low-grade laminitis or metabolic issues, you will have a sore horse with less than optimal feet.
I am NOT one of those people that soaks their hay and denounces grain. I actually give my horses a little bit of sweet feed each evening as a treat. But I don't have grass and I've never had to maintain a horse on grass either. I'm sure I would be always worried about laminitis if I did. I just think the growth rings are note-worthy. If I personally were shoeing this horse, I would bring the heels down AND bring the breakover back. Something like a Natural Balance shoe. Then the frogs would get stimulus from the ground and the horse would have some breakover.
As for barefoot, I have been on both sides and consider myself pretty neutral.
I took farrier science, learned everything I could, watched a lot of farriers and shod my own horses for probably 8 or more years.
Then I had some health problems and wasn't able to shoe for a while. I went on the Internet and discovered that a lot of people believed in barefoot and decided to try it for myself.
My Mustang, whom was shod for years when I bought him, transitioned GREAT from shod to barefoot. Maybe because he wears a size 2 shoe (nice, big healthy feet) and had a good barefoot start in life since he was feral.
My Paint, whom was in his 20's at the time, never did do well barefoot. I always had to ride him in boots. He's barefoot now, but that's because he's 30yrs. Old and no longer ride-able.
My Arab did really well barefoot for the most part.
Barefoot works GREAT if you don't have to ride on rocks. If you ride on rocks, it is still possible, but I find myself always worrying about the rocks even if my horse seems to handle it okay. I usually use boots if I think I will encounter tons of rocks on the trail. But my Mustang is basically able to go anywhere barefoot now, wether his Mommy worries about it or not!
It did take over a year, maybe more like two years, for him to get really tough feet. In the meantime, Easyboot Epics were my best friends. I am not convinced that all horses can get to the point of riding barefoot in the rocks without hoof boots.
(on soft ground, yes). But even if I am not sure a horse will make it to that point, I plan to keep doing it because I do think it is healthier for the foot to be without shoes 99% of the time. And then if I am riding the horse in the rocks, I will use hoof boots. So I think I am barefoot to stay, even if it means booting the horse in rocky terrain.
I think keeping the horse on the terrain you plan to ride on is the key to getting good feet, but my pens simply aren't big enough to give them enough movement and keep them out of the mud in wintery weather. So probably some of my barefoot limitations are due to not having a big enough turnout area for the horses to move around in. I did try the pea gravel but most of it sunk to China!