When all those threads synchronize frequently, like every frame in a game, you will encounter difficulties.
Here's where I can agree that E-cores present challenges, but it's mostly because threading APIs aren't sufficiently expressive for the game to give the OS guidance on how the threads should be scheduled. Also, because a threading-oriented approach encourages games and other apps to spawn more threads than they should, which will almost certainly have some of them land on E-cores.
However, that's a problem with scheduling and not with the E-cores. Gamers have indeed found that some games run better with E-cores disabled, with hyperthreading disabled, and sometimes with both disabled.
The principal being that you have a hard time determining the size of the workload to give each thread when execution speed may vary from 50% to 100%.
The normal approach to that is just to partition the workload into small enough chunks that it's easy to effectively load-balance.
In my experience, the OS trying to automagically decide stuff without all the relevant data always lead to subpar performances and crappy behavior.
That's why Intel created the Thread Director, but I think it was an imperfect solution and what we really need is to stop treating threads as an all-purpose building block for exploiting concurrency.
The fact is that this e-core business (and c cores from AMD) is a specialized hardware, and as such its use may be useful but in my mind it has also drawbacks, that some people just don't want to understand.
C-cores are mainly just frequency-limited versions of the fullsized cores. If you only involve them when the fullsized cores' clocks get throttled to near the peaks of the C-cores, then they carry no significant deficit (other than less L3 cache).
And laptop sales being 60% higher than desktop play a major role in this "optimization" coming to dektop.
By itself, the desktop market is more than big enough to justify Intel's S-series dies. There's no need for them to compromise their desktop platform, just to cater to high-end laptops.
In fact, I'm pretty sure they sell way fewer HX laptops than they do mainstream desktops, because most people don't want a big, heavy laptop with terrible battery life and a loud cooling fan. That's what you get, when you put their desktop CPUs in a laptop.