Nail on the head, nail...on...the...head.
Just to add for the benefit of others - If these are “completely separate” races, then there should be no official “Triple Crown” title. Since there is, as in every other sport, competition should be structured to support running in all three races that comprise the sequence. The equivalent would be allowing a runner to sit-out until the final race after other runners have done qualifying races. It seems odd to me that horse racing is the only sport to allow this.
HORSE-racing is also the only sport wherein the object of award and honors is the horse, a non-human.
One simply cannot make horses run in every event. They do not know what is happening, that there may be a schedule to hold, nor can they tell you if they just aren’t right. It is not at all the same as any other sport which involves humans or even other horse sports where the human gets the credit.
This silly proposition means every Belmont will be 3 horses because they cannot all hold nor can any organization tell a horse he must run, risk of injury be damned.
The Triple Crown is a mere icing on the cake. It is an artificial construct that grew out the importance of 3 stakes which happened to run annually near in time, and a desire to copy the English construct. Each is important in itself.
Horses are chosen for annual awards by polls of fans and journalists. There simply is no play-off system. Nor is there one for the college football either. Not only can you not compare horses to humans, but you most definitely cannot compare it to team sports. Racing is a pure sport, being individual rather than team, even then it cannot be compared to human athletics.