I have to disagree again sorry. I can't speak to being able to "spot a unity or unreal game from miles away," but if you want to make a game, make the damn game not an engine.
I get the feeling there is a serious survivor bias happening here. Individuals who are talented and knowledgable enough to roll their own engine, make it well and quick enough, maintain motivation AND cross the finish line to actually make a game likely make a pretty good game. Now consider all the other people who tried this path and got stuck along the way. Now you're gonna recommend all that complexity and difficulty to someone because you think games should "feel" unique. Like, its just not based in reality sorry.
I think there are 2 reasons to roll your own game engine
1. Making a game isn't your top priority and you're interested in game engines
2. No existing game engine does what you need it to do and you have enough experience/knowledge to know where you're going
If you're decision is based on "I want my game to feel unique", "it might not be performance enough" or some other immaterial and ethereal concept I fear you're gonna be set up for failure.
Noita is a perfect example of when to roll your own. They push the boundaries so much that they absolutely need a custom engine. Path of Exile, another example where their vision REQUIRED a custom game engine.
I started out writing my own engine. Never finished a game. Switch to unity and finished two then hit industry.
Both games were mediocre if I am generous.
The janky demos i made with the custom engine felt and looked so much better. I even had folks on forums asking if they could join the project.
The issue is if everyone uses the same unity standard shader, lighting, posteffcts, etc, it ends up with a certain smell. The effort it takes to work around this requires implementing the version of the given components that better match the vision. Most custom game engines still use a plethora of libraries replacing the ones that matter. It also isnt so binary. Earlier box3d post was literally catalyzed by Unreals physics engine lacking some 3 line of code.
I think what you are really speaking to is that few people have the discipline or motivation to complete anything. The two games above that I completely were in a large part because i actually sat down wrote a design doc, made a schedule, and stuck to it aggressively reducing scope.
I recently wrote an article showing just how easy it is to make a game engine using css box shadows as the renderer, web audio, and a stupid simple tween system. I think it illustrates pretty well that people vastly overestimate what a engine is.
Edit: https://dgerrells.com/blog/how-to-make-a-game-engine