Anebel, I see entirely what you mean in terms of his scores - at the level he's competing at, not only is he one of very few of his type but he isn't performing all that well compared to the Warmbloods at the same level. Ultimately however well he does, he's fighting against his build and his breeding to get to wherever he gets to, which will always be a disadvantage that the Warmbloods don't have. My friend was heartbroken on reaching Medium level with her TB and realising that, no matter how hard her mare tried, she just physically couldn't make the jump to Advanced Medium because she was fighting against her own build, and she wasn't a draft cross!
And yes, most people will never reach PSG/GP, which is a very valid point. But how far *does* the OP want to go? Competing up to Elementary should be possible for most breeds allowing for decent conformation, willingness to work etc. But Medium? Advanced Medium? These are perfectly possible aims for a rider without worrying about the expense/pure luck of getting to the higher levels, but require a horse with talent - not achievable by every horse by far. Finding a draft cross or tbh a QH, TB, Welsh Cob, anything really that isn't bred for dressage that has the potential to reach those middling levels is going to take an eye that a rider who hasn't yet reached those levels (and in the OP's case perhaps hasn't even that much experience with the breeds) might not yet have. So if the rider is happy in the lowest levels, and REALLY doesn't want to see how far they can really go, then it doesn;t matter either way - the type of horse you choose shouldn;t have anything to do with dressage ability, as it's not really the deciding factor. However, if getting to movements like half-pass, pirouettes and flying changes is something that the rider wants, then why limit yourself when you could have a dressage bred horse?
Without all the bickering, ultimately it just depends how far in dressage you want to go. A good draft cross with conformation for dressage, a good attitude and no physical problems and good solid training could do well in the low levels if that is as far as is required. Getting to those middling to high levels, it may be possible, but it depends on your priorities - and be prepared for it to be too much for the horse.