Those folks who are raised with horses, have little problem with riding them, with or without saddles. For those who first attempt to do so as teenagers or adults, will probably have quite an adjustment to endure. For such people, it is their choice to expose themselves to such challenges, and judge for themselves if it is worth the effort and risk of permanent injury and embarrassment.
Also their choice whether to expose their horse to prolonged exposure to weight over a small area, potentially creating pressure points and damage to the horse. Hence the invention of saddle trees to distribute pressure over a wider area, increasing comfort and saftly for both horse and rider.
As to Seiza. I have soem knee issues so I can only sit seiza for short periods of time. If it seems that sensei will be speaking or demonstrating for more than a few minutes I sit cross legged. Fortunately he encourages us to sit comfortably rather than risk injuring ourselves for the sake of tradition. I have noticed that my tolerance for that position is better now I have been training for a while than it was at first.