Lower level dressage, the level at which most amateurs are going to ride here in the UK, is filled with Welsh Cobs, gypsy cobs, New Forest Ponies, the hairy thing that lives out in the mud all winter … and currently the fastest growing division is OTTB dressage. We frequently have national champion Welsh or hairy cobs.
It is only when a rider decides that it is only dressage and nothing else and then seeks to rise to the upper heights that the WB comes to dominate.
As the discipline of dressage comes to be understood with greater depth, the non-WB comes to shine because there is greater ability to train a TB or a cob or a pony appropriately.