Too much subjectivity and art involved in dressage and not enough raw athletic talent.
I’m sure there are lots of skills involved in dressage but they don’t produce objective measurable outcomes.
Actually, at this level the judging criteria is incredibly strict and they’re looking for very very specific things – even down to the angle and extension of the horses’ legs during certain movements – and there are seven judges around the arena, the highest and lowest scores for each movement being discarded and the remaing five averaged.
As for the cost (which I’m sure has been done before) – other half’s latest horse is an ex-racer that came free (to a good home!) from the trainer, but a good allrounder can be had at £2k easily. Clothing can be on a par with cycling clothing costs. DIY livery can be had for £10-£35 a week, feed/hay/bedding/etc about £20 a week, a good old-school leather saddle can be had for £250, bridles start at £25. Competition entry starts at £10 for local riding club stuff, affiliated starts at £15.
Granted it’s not the cheapest of pastimes but it’s far from deserving of the elitist, rich-people-only tag that it gets lumbered with. Yes, you can spend far, far more if you want but it’s not mandatory.
The difference between riding and cycling comes in that you need lessons with horseriding if you want to have any chance of doing it safely and correctly. Get a jump wrong even at the lowest levels and you can be looking at serious injury, not to mention causing the horse pain by not riding it correctly.
As for Olympic dressage looking easy – that’s the point… ;) I’ve been riding a few years now, and I couldn’t even begin to ride even one side of those horses – they’re performance athletes in their own right.