Wait what? We have no problem investing those points. It just takes until level 31. But I know a good few HA who can use Arabians.
And were you here when they were used by just about every decent lancer? They were a lancers horse, not an HA's horse.
Power draw, horse archery, riding, WM for WPF in archery as well as for a melee weapon... That's a lot of points to dish out. That sounds like a big deterrent to investing extra points in riding just for the particular horse. Sure, if you don't retire you'll get the points you need eventually, but that's true of almost any build.
And if HA can't use the Arabian till they are very high level, while melee cav have no problem getting it early and were never really bothered by the attribute point investment, then I'd still say that these cav have the riding cost they do just to make it tough for HAs to have them. After all, why would all the heavy cav be only 5 riding, even though they are probably more valuable to melee cav than these lighter horses. I'd say it's because these heavy horses don't really offer any advantage to HAs.
I used to use an Arabian quite often as a lancer. But that was back when archers weren't so ridiculously powerful. It's not a lancers horse now if you actually want to play the game and not have your expensive horse 1 shot because an archer pointed a bow at you.