Be interested to see some hoof/horse pics(check link below) too & more info. Is he comfortable on any surfaces? Is he particularly uncomfortable/lame doing certain things - like on a circle or such? - Obviously he'll be worse on stony ground. What in that way has changed since shoes? Did the vet mention anything else with regard to lameness & those rads?
Agree with Trinity & mostly with Clava. Disagree strongly with Amazin, except in not just taking anyone's word for it - especially but not only on an internet forum - blindly. Just because someone is a vet doesn't mean to say they should be taken on blind faith either IMO. I won't start on 'necessary & proven practices' & racehorse's feet.
I agree fully about diet for starters - get him off grain/starchy feed & onto a healthy, low starch diet. Good, well balanced nutrition also plays an important part & something like feedxl.com will help you work that out.
'If you don't use it, you lose it' is an appropriate saying to keep in mind regarding horse's hooves. Just like you'll lose - or you won't develop - the callouses on your feet if you only ever walk bare on shag pile. Of course a 2yo will have little to lose, because he won't have developed that much in the first place, particularly being stabled all his life.
Even in 'ideal' situations, horses don't *begin* to develop their caudal hoof(digital cushion, etc) until around 4yo. Unfortunately, due to living environment, shoeing, etc, many domestic horses never do & have a squishy, weak 'foals' DC throughout life. That is one reason why I disagree with shoeing a horse under about 6yo min.
Re shoes for this problem, yes, they can help the horse *be more comfortable*, but without pads they provide no protection for the thin soles, and peripherally loading the foot, especially without providing support underneath tends to cause them to become thinner, among other things. So if you are going to shoe, I'd at least be filling his feet with Vettec or such. But I'd be inclined to use padded hoof boots(or even just Vettec Soleguard alone, as he's not yet in work, so it should last reasonably when he's just in the paddock.
His soles don't need to be harder & more brittle, but they need to *grow* thicker. Therefore I wouldn't bother with the paint, but I would be protecting & supporting them.