I wouldn’t pick a downhill, halter type QH, but as already mentioned, there are plenty of nice, sport-type QHs, Appies, and Paints. All these breeds come from TB breeding stock originally. There are plenty of them out there in the Hunter, Eventing, and Dressage world - often shown as PHR so you don’t even know what they are.
As for the cross to WB - Old/ISR and RPSI both approve the mares and register the offspring as long as the stallion is approved for breeding with them. Several breeders have been doing these crosses, some are multi-generational at this point with good success.
I know someone who went I-1 on a Swedish/QH cross, and someone else who has bred a couple of Appy/Hanoverian crosses that have done well - one was just bought by an A circuit jumper rider. I bred to a Paint mare to Cadence and got a really nice moving mare who has just started jumping and has done well at her first show. And she had a great brain! Silverwood use to have a stallion who was part Paint, and was a nice hunter stallion.
Again, I wouldn’t pick the halter type stock horse - why fight that conformation? But there are so many nicely built, TB types, and they often have great brains, better then the TB.