I would argue there is quite a difference between your draft x and a proper TB/ID. Or, there can be. The Irish Draught, particularly lines still in Ireland, are not going to be nearly as heavy and likewise the TB cross often produces a cross that very much looks like a sport horse. (I actually own a traditional Irish horse, whose right under 25% Irish Draught and competing at the 3*** level. Said horse did have many zero’s in purchase price)
It could be not that your trainer has a bias against the breeding of a horse, but the level/your ability to produce such horse. I would assume even a draught cross, that is amateur friendly, already has the flatwork, bravery, tidiness, soundness, balance that enables an amateur to safely navigate novice is likely not a cheap animal. (In my southeast/Area III area, that horse is mid-fives)
Could it be those types you’re looking at are also green and missing some training buttons if they’ve been on the back-burner? Rather, a warmblood, the ones your trainer has access to, has been produced since riding age, already possesses traits that will be easier for an amateur to produce? That is worth its weight in gold.
Just thinking out loud.
I’ve started many horses for amateurs. It’s heart-breaking and frustrating. Client very similar, bought a rather cheap, 4yo draught x. If this horse had been handled from foaling, started a little younger, been out and about, one the price would have been triple and maybe a fit. But, the horse hadn’t been touched at all likely since birth and was forcefully pushed in trailer and arrived at my farm. Yes, I started the horse under-saddle, but then also due to budget in 30-days went back to amateur who was nervous and we ended up selling in 6-months after the horse bolted and rider fell off. We replaced with a very boring looking but safe TB. (I tell my amateurs, buy boring. We can stick a bonnet on them and it’s not boring when you and your daughter confidently finish course alive and in the ribbons)