This leads to other questions: do our posters crave complexity? Are simplicity-seekers less likely to be posting at ENWorld? Where's the desire for elegance?
Elegance is about making a system no more complicated
than necessary.
I used to be all about elegance in RPG design. I've come to realize that it is monstrously overrated. It leads to simplifications that are too clever by half, and vital distinctions being papered over by too much abstraction. It isn't that one should never seek elegance, but it is very much a "nice to have," a pleasing but nonessential attribute.
Mounted Combat: mounting and dismounting cost 5 feet of movement. While mounted, your speed becomes that of your mount, and you can choose to make Attack actions as yourself or as your mount.
This is the sort of solution 4E tended to adopt: Take the "standard use case," boil it down to the simplest possible implementation, and just ignore all corner cases that arise out of it.
5E quite deliberately moved away from this approach, accepting a bit more complexity to better align mechanics with fiction. For example, this neat simple solution runs into problems as soon as you have a mount that can think and act on its own--which is not at all unusual in D&D. If you jump on the back of a dragon, does it lose all free will and become a passive vehicle as long as you can claim to be "mounted?" If not, what's the dividing line between a "mount" and a "creature whose back you happen to be on?" Follow this logic and you end up with the "controlled versus independent" distinction.
And then there's the question of multiple riders. Suppose you and I both mount the same horse? On your turn, you move 60 feet (the horse's speed). On my turn, I move another 60 feet. Having two riders makes the horse twice as fast. Crowd four halflings on the horse's back and it can go like a Formula 1 racer. Obviously, this makes no sense--only one of us can actually be the "rider" in control of the horse, everyone else is just a passenger. So now your clean simple rule has developed another nasty complication, where you have to distinguish "mount as the rider" from "mount as a passenger."
Next up, what about terrain hazards? If you gallop into caltrops, who takes damage, you or the horse? By your rule, it's you--you're the one moving. So there needs to be a clause about terrain hazards affecting the mount. What happens if you move into a space that you can fit into but your mount can't? Nothing in your rule as written would prevent this. So you have to add another clause that the rider's size changes to match the mount's, which has assorted side effects (e.g., grappling).
As the weirdnesses keep piling up, it quickly becomes simpler to reframe the whole thing in a way that matches the fiction: The mount is the one doing the moving. If independent, it acts on its own turn. If "controlled," it acts on the turn of whoever is controlling it.
And, just like that, you've arrived at 5E's mounted combat rules.
