All of this is true and has been true for decades in the game industry.
The other side of this seesaw is: Games are fundamentally in the novelty business. Players like some amount of familiarity, but they want new experiences. Every game engine has a sort of "grain" to it where it tends to produce games with a certain look and feel. The flat-ish shading and floaty physics of Unity is a particularly visible example of this. So using a widely used game engine can put you at a disadvantage if you're trying to make a game that doesn't go with that grain and offers players something different.
As more studios consolidate on the same engine, more players will get tired of that sameness and reward other studios more. As more studios do their own thing, players will become saturated with novelty and the benefits of not using an engine will go down. There is no stable equilibrium.
I think there is another benefit of a custom engine — you built it to fit your workflow, so you could be extremely productive with all kinds of tools built specifically for this workflow. UE or Unity do not consider your specific cases.
The problem is that companies are not willing to groom new engineers to get familiar with the code.
> Every game engine has a sort of "grain" to it where it tends to produce games with a certain look and feel.
I think this is a bit of a myth. Unreal gets this criticism a lot, but it's usually because many studios choose to stick close to the rendering defaults, which does lead to a certain look.
To that point, it's probably a lot cheaper to configure Unreal or Unity into a unique "grain" than it is to develop your own engine. It's also possible to use custom physics instead of those built into the engine.
> Every game engine has a sort of "grain" to it where it tends to produce games with a certain look and feel. The flat-ish shading and floaty physics of Unity is a particularly visible example of this.
Ridiculous and provably false.
It's like saying "every novel written with a typewriter tends to produce stories with a certain theme and dialog"
You're right, but idTech is almost by definition that "novelty" kind of engine. And it did help id to sell more games. It's just apparently not enough.