Except the cost to acquire cavalry is so much more. You are literally paying for the extra map speed. There are also perks that can massively bridge that gap, and the right combination of perks can have you moving much faster through forests with “mounted infantry” versus a cavalry army, which moves significantly faster in open expanses in the east and south.
Part of what makes a good sandbox game exciting is risk vs reward and pros/cons choices. Cavalry are expensive and wasted on sieges, but move quickly on the map and offer more tactical options. Infantry move slower but are cheaper to produce, and the Mount/footman combo generates more carrying capacity.
And let’s not forget that you don’t just expend one horse on the entire line, you expend two horses when training from scratch, and hiring mounted troops with a horse is quite a bit more expensive as well.
So please, do not turn this into every other game where there is an “obvious” choice and 100% foot soldier armies are strictly better then mounted ones all because a handful of players wanted the upsides both had to offer wrapped into one. I don’t think you were being fully honest on the bullet point, even though you claimed you were. Do you want to get to the siege faster? Or do you want to use the more cost efficient troops?