It might well be simpler and more intuitive, but since you're asking in the Rules Questions forum: that's not what they have.
Qadiran horselord cavaliers don't get to use all the assorted rules that charges get (pounce if they somehow have it, partial charge when staggered, spirited charge damage multiplier, flinging charge if they have that, special effects which trigger on a charge etc.) with their move-attack-move ability. It's not a charge.
Spring attack is more limited, though improved/greater spring attack can improve it slightly and wouldn't apply to a charge.
Wrong forum - rules questions is about the rules as they stand. Homebrew and house rules or possibly advice or general discussion are the forums which are for potential rules changes.
Since you're asking though, from a gameplay/flavour perspective the issue is more about the potential multiple attacks on one target (or one large spirited charge or vital strike attack) that a charge allows vs. the single attack per target that spring attack (inc. imp/greater) allows.
I suspect that the designer was aiming for a single attack intentionally. That isn't amazingly effective in PF1, but OTOH with enough room and speed a horselord can cut the enemy to pieces if they get multiple attacks vs. a single readied attack each round. On the gripping hand - in the same situation a mounted archer just wins. Making it a form of charge shouldn't make the balance any worse than it is currently.
Considering how f~#+ed up Ride-by Attack is, everyone should be glad they didn't use that feat. Seriously, RAW, Ride-by Attack doesn't change that "You must move to the closest space from which you can attack the opponent", which means in order to use the feat, you'd have to ride through the target, something that the rules explicitly disallow unless you use the overrun maneuver, which you can't use because it requires either a standard action or to be used during a charge, and your charge has just ended when you reached the target and made the attack.
Flavorwise, Spring Attack is a much better fit for "skirmishers, ducking in and out of combat".
I do think the whole ability should be different, allowing a charge action with the ability to use any unspend movement to go back the same way after the attack, if only to make it compatible with the Sand Storm ability - mutually exclusive class features like that are horrible design. I wouldn't make it reference any feat. Paizo just loves referencing other rule options way too much - compare Flurry of Blows and Brawler's Flurry referencing/using the TWF rules despite not using two weapons. Considering how the archetype grants the benefits of Mobility but does not remove the need for Dodge and Mobility as prereqs for feats, the "counts as Spring Attack for prereq" part is worthless anyway, so losing that isn't an issue. Add a "can only make one attack as part of the charge" line to avoid potential abuse, and it's all good.
Rules for Mounted Combat are that Mounted Combat doesn't work. -Paizo, 2011