Well, there are the lay-offs, hiring freezes, pay freezes and...oh, wait you are talking about the game mechanic. Okay.
I only use morale for mass combat. When you have groups of employed or pressed into service. Morale is not the same as fear and not even the same a loyalty. There are other mechanics for fear in 5e. Also, I see HPs as including your mental well being. You can literally be beaten down and finally can't force yourself to go on. So fear, hit points, and also exhaustion--plenty of ways to make characters "give up" in an adventure until they get some R&R. I've used loyalty for hirelings, especially when the party has a ship or business from which they may be absent from for long periods of time.
Morale is best used as a tactical resource--a measure of how close a combatant is to giving up in a battle or in a war as a whole. For gaming purposes, I use the secondary, more narrowly scoped definition: "a sense of common purpose with respect to a group : esprit de corps The ship's morale improved after two days of shore leave." (
https://www.merriam-webster.com/dictionary/morale). Do I need to determine at what point combatants will go AWOL or surrender and how many in a group do so? Morale is a nice mechanic for that.
But it just has not come up in my 5e games.
I did, however, back Matt Colville's
Strongholds and Streaming Kickstarter though. I'm looking to bring castles and mass combat into my campaign and I suspect I'll use morale at that point. Whether I use the optional rule in the DMG depend on whether Matt offers something better.