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.
UE is also just not a good engine. If you reduce "what is a 3D game engine" really hard it is "framework for running an input-process-output loop while consistently rendering audio and video". UE fails at the latter (factually unfixable shadder stuttering issues). A pragmatist might consider the taxonomy and say UE is therefore not a game engine. Unreal seems to be a great framework for assembling and generating content, though. Maybe Unreal Free was the metaverse all along?
Meanwhile idTech certainly had issues, mostly in regards to dynamic levels, especially in older iterations, but "consistently rendering audio and video" was certainly never among them. It is well above the industry mean when it comes to the core of what a game engine is.