You also have to ask what your goal is with fatigue.
If your goal is to simply make the player stop using units they like using, then, okay. Fatigue is a great way to do it.
However, based off Onmi's writeup, it appears his goal is to make the player diversify the army a little more. If you force me to stop using a unit because they suck for a chapter thanks to a number on their screen, I'll be annoyed, especially if I really like using the unit. However, if you keep other, less-used units competitive, then I always have incentive to try them out. For example, suppose you're playing FE7 for the first time, and you're using the following units:
Hector, Serra, Matthew, Dorcas, Bartre, Erk, Lowen, Guy.
Several chapters into the game, you get a cool new unit. Her name is Priscilla. Now, you like Serra, because of course you do. She's fucking awesome. However, maybe you want to try out Priscilla for a while. You drop Serra for a chapter, and put Priscilla on. She performs quite well! After three or four chapters, Serra starts to fall behind in levels, and let's say 6 chapters pass or so.
Now, on this chapter, let's say Chapter 17 or so, you glance at your units. You say, "Man, I liked Serra, but she's so weak now. Guess I'll just keep using Priscilla."
Two chapters later, fatigue kicks in. Priscilla is going to be weak until you ditch your main healer for a chapter. You say to yourself, "Goddamnit, now I have to use someone else."
Are you more likely to use Serra? No. You'll probably go for Pent or another equally good candidate. Serra is too weak to be usable. So you pull out Pent, and you're like "Hey he's not bad, maybe I'll use him for a chapter or two!"
Three chapters later, Pent outclasses Priscilla. You say, "Oh well, she's just not as good as him anymore."
Eventually, Pent becomes fatigued too, and the process starts all over again.
Now, honestly, Serra is the worst candidate for my example, because Healers don't benefit much from a bunch of stats like a combat units does. Guy<Raven or especially Lowen<Sain/Kent would be a better comparison, but hopefully you get my point.
Had Serra instead just kept competitive by getting a bonus every chapter or two, you'd always be able to at least say "Hey, she's not worthless, maybe I'll try her out for a chapter or two and powerlevel her since Prissy isn't getting much EXP from enemies. She has +3 in all stats for this one chapter, so she isn't woefully underpowered!"
In Fire Emblem, if a unit sits out for a few chapters, they're basically fodder for the rest of the game. Think of how FE9 and 10 solved this with BEXP. By weighting the BEXP for lower leveled units, they allow you to try out different units in your army that you normally wouldn't. By giving less BEXP for higher leveled units, they forced the player to say, "Well, Oscar is already really good, so I might as well level up Mist a bit. Having a second healer on this chapter might prove useful."
It's the same principle as BEXP, in that the idea isn't "Punish the player for playing how they like" but instead "Reward them for trying different units out."