I would say that it has fallen out of favor, because it appeals to a specific playstyle that is not particularly popular. Having it as an optional rule is just fine, because it's easier to add things in than take things out of the 5E chassis.You are so right. I should have looked more closely.
Still, I'm curious why it's an "optional" rule and somewhat vaguely defined. And Intimidate isn't even mentioned.
It seems like Morale has somewhat fallen out of favor. Is that true?
Technically, the default is not that enemies fight to the death, but that the DM determines their actions. Hopefully this is based on specific situations, such as the creatures motivations, courage level, intelligence, and current health. If DMs are lazy and just have creatures fight to the death, adding a morale check isn't going to change that (it didn't in prior editions either).
The problem with morale (especially the current version) is that it could often create very weird situations where the enemy flees while winning. This is why I use a modified system that is rolled only at specific times, using the DMs best judgement. Taking out a leader, dropping a boss monster to half HP, or making an Intimidation check as a bonus action may trigger this check (encouraging tactics to use these things), but since everything is at the DM's discretion, it may not occur. This keeps stupid situations from occurring, but remember that they don't know the PCs HP or resources. Thus sometimes creatures may flee if they are "winning," but they simply don't know it (just like PCs may flee from an enemy on its last legs too).