I get the impression that the powers that be in the pentathlon organization liked having the equestrian phase not because of any great appreciation for horses or horsemanship, but because it was a great way to shake up the leaderboard.
Someone who’s a good runner could have a slightly off day, but overall the running results are going to be pretty predictable. Ditto swimming … shooting and fencing maybe a little more variation, but you can probably still predict the top performers pretty well. Equestrian depends a lot on the horse, so it’s a way to make the competitions “anybody’s game” … maybe someone who’s not the fastest or the best fencer is fortunate enough to draw a horse that’s a true heart-of-gold packer and will schlep them around a 4’ course in one piece come hell or high water. Maybe the person who’s a shoe-in to be leading after the other phases draws a horse that needs a bit more help and their riding skills aren’t up to that challenge. And so on…
Edit to finish my thought: keeping riding, but making it easier on the the horses (i.e. lower jumps) would necessarily make it “easier” for the riders in the sense that the vast majority would at least get around the course. So it would no longer be the scoreboard-shaker-upper it currently is. Sure, it could be turned into a judged equitation round to keep everyone from getting through with no effect on the leaderboard, but it would likely still be less of an “equalizer” and adding subjective scoring would change things pretty drastically.