Any politician (or bureaucrat) who says "you know, maybe we should be denying disability to 20% of these veterans" is going to be strung up and quartered. So, nobody tries.
Not saying grift is excusable, but there's a lot of checks and balances on this system – not the least of which if a veteran is caught lying, he loses his benefits and may even have to pay them back.
If you claim PTSD, trauma, or back/knee/joint pain without fabricating the material circumstances of your injury (lying about where you were stationed or what you were doing), there is a 0% chance you will be accused, much less convicted, of lying.
Look for a single vet disability fraud case (and there aren't many, period) where the conviction was for anything other than outright fabrication of service record.
But that's just a specific issue relevant to my time in the service. The bottom line is that unless you report every little thing that _might_ cause an issue later, you're going to be up shit creek when you get out and find out that something you were exposed to during your service is causing an expensive medical issue that you have to deal with. There are all kinds of fucked up things people had to do while they were in, that they struggle to get compensation for now that the consequences are catching up, because the issues aren't straightforwardly attributable to some event during your service, like with combat injuries. Burn pits are the most notorious one - you have advocates like Jon Stewart fighting in Congress to pass laws to support vets who were forced to work those pits and are now battling all kinds of complications. If anyone should be an obvious beneficiary of the disability system, beyond those with combat injuries, it should be those folks - but they are largely left hanging in the wind. In the case of burn pits especially, the military _knew_ there were consequences to having soldiers work them, but chalked it up as the cost of war.
Frankly, from what I've observed, once vets are out of the service, our country largely gives them the middle finger when they struggle with mental or physical health issues. I say "them" here, because I'm not a combat veteran, and I'm lucky that I had it pretty easy during my tenure (2009-2015), but for many, that is very much not the case. Yeah, nobody in Congress is going to stand up in front of everyone and say "let's make disability benefits harder to obtain" - but I have no doubt they'd have few, if any, qualms about doing it behind closed doors.