I beg to differ. QQQ, being weighted by market cap, has a structural advantage over QQQE by design...

Sure, it is by design.
(QQQ isn't cap weight, by the way, but it's similar)
Cap weight was designed on purpose so that there would be minimal trading, not because it's the optimal way to invest for the investor with capital at risk.
As prices go up, there isn't any trading to do, so it's cheap and easy to run a fund. That's the reasoning.

The thing is, the very largest firms are generally the worst investments.
If anything large is currently wildly overvalued, it will be found among the very largest cap firms.
There are companies and years that are exceptions, but that's the general rule over time: that's where you go to look for stuff that's overpriced.

The S&P 500 is (basically) cap weighted, and suffers from this problem a lot. That's why almost any other weighting from the same firms works better.
But the largest 5 firms do even worse than cap weight of the whole set.

Figures done with a proxy database, might be off by 0.1% or so:
Not bad: the S&P 500 equal weight, all 500 equally weighted, CAGR since '97 = 9.32%
Bad: the S&P 500, float adjusted cap weighted, CAGR 8.49%
Worst: the biggest 5 of those by market cap, then equally weighted: CAGR 8.08%

It's not luck if you truly understand the nature of these businesses.

For sure.
As I mentioned, if you truly understand the nature of the very largest businesses and like their prospects and pricing, I agree, buy them.
I have owned some of the largest ones.
But then, in that situation, why buy the other 90-95 stocks? What's the point of QQQ?
Surely someone who knows the few giants very well will know which of them is really the pick of the litter, so you wouldn't want all of them.
I don't know what the future returns of (say) Alphabet and Nvidia are from here, but I imagine they are going to be quite different.

A cluster of very large cap firms, simply because they are the largest, is a very poor wager indeed, despite recent good results.
As was the case 25 years ago, I find it best never to confuse recent history with a law of nature.
If there is a general law of nature, it's to avoid the very largest.

Jim