The problems in MP are longstanding - if you include riding, it essentially becomes an extended Equestrian event (that was, originally, uniquely, solely for actual cavalry officers which is a giveaway of the element at the heart of the sport) with all the universality problems that creates - worse, while a small nation might produce one or two accomplished horsepersons with their own horses, MP insists and depends on strange horses being volunteered to be ridden by non specialists - often from countries with no equestrian tradition at all - and therefore not much in the way of horses to practice on.
And when you have problems even with strong equestrian nations like Germany, it simply highlights that, fun and exciting as the jumping element can be, it's kind of like the famous description of the Charge of the Light Brigade - 'c'est magnifique, mais ce n'est pas la guerre' - it is magnificent, but it's not war. Well, increasingly the showjumping was magnificent, but it was not sport, it was 'it's a knockout/jeux sans frontieres' - the excitement was who would get the dud horse. Ninja Warrior looks silly in a sports context, but no sillier than the riding sometimes did.
So, given it was no longer a military only event, it had moved away from the original de Coubertain idea anyway - and de Coubertain's whimsy is the only reason the sport exsts and is still has its spot in the Games. how do you preserve at least an idea of it? Well, you need to look, I suppose, at what the heart of the sport is, what is it really testing.
If it's really an Equestrian event, then it ought to be run as such - probably using athletes own horses - indeed, the three day event has an odd element of it as it is, because if you step back, Eventing is a way of basically getting cross-country racing/steeplechasing into the Games, at least in a kind of mini TT format.
Once you allow civilians into MP, you already change the nature of the challenge - it is no longer testing actual cavalry soldiers as originally designed by PdC. So either the point of the sport is gone, or you find a slightly new point. The new point, I would argue, was to create an event of five deliberately very different disciplines which in some sense echoes the theme of the escape of a soldier from enemy territory. And to do so without the increasing farce of strange horses, which the IOC were simply not going to tolerate.
Personally, in terms of 'escape of a soldier' and 5 very different disciplines, I think the balance is slightly wrong - a laser run AND an obstacle course seems to make running an element twice over. If it had been me - mad as it'll sound, I'd have leaned into the combat theme - we already have 'sword and pistol' - why not add 'bare hands' - a truncated form of judo (a kind of bracket ranking system or swiss system for a limited number of golden point bouts), for example, and then move the obstacle course element into the Laser run - the added idea of course being that the unusual exertions of the arms will affect the shooting, as it would in an actual escape.
So now your event is -
swordfight your way out of the battle,
swim across a river,
fight unarmed an adversary you encounter on the other side,
take his pistol, then run across country and around and across obstacles, and hold off enemy with the same pistol
before reaching the border.
As for Equestrian Pentathlon as we would presumably now call it, that sport may be preserved outside the Olympics by UIPM, perhaps included as part of the World Games, or even the Continental Games in the IOC tradition. Hell, it may even return to its older, more traditional format of separate running and shooting.