Subject: Re: OT: Buying random stocks (monkeys!)
As you might expect, I have looked at a lot of these questions.

Would random selection of QQQ (or Nasdaq top 200) work as well? a kind of Monkey meets QQQE?
Probably so. I have done most of my testing on the Nasdaq 100 equal weight (both valuation and returns etc).
More or less by construction the outliers can't matter that much, so a large sample will resemble the whole quite closely.
But one thought: the turnover is pretty low.
Other than a lot of typing the first day of your portfolio, why not buy 'em all?
Just a thought.

Is slightly "stacking the deck" (selecting a subset of the general market: highest ROE, lowest debt, etc.) helpful or should one be a neutral as possible (pick from SP500, SP1500 or Russell 1000)
I have found no benefit from stacking the deck within the Nasdaq 100 set.
From within a broader market set, yes.
I have looked at Value Line 1700 set because I have a good database for that, and also sometimes in the S&P 500 set.
The best single/simple/defensible criterion I have found is high ROE.
Since I often test using the field in Value Line that is from the most recent annual statements, the turnover is again very low.
You can use other criteria that work better in backtests, but going too far down that road rapidly leads to disillusion if not madness.
The underlying overgeneralization logic is roughly this: Not all high ROE firms are great or safe businesses, but all great businesses have high ROE.
By picking only high ROE firms, you're going to get some losers, but you are eliminating a LOT of dud businesses. Fewer duds means better average returns.

Sample numbers:
Numbers below (except as noted): portfolio reconstructed and equally weighted quarterly, without trading costs, from within the Value Line 1700 set of firms,
using Value Line [annual] "Return on Shareholders Equity" field, dividends reinvested, no tax provision, 20 years to end 2022.
All of the Value Line 1700 stocks: 11.74%
S&P 500: 9.48%
Top 30% by ROE: 12.57%
Top 20% by ROE: 12.79%
Top 10% by ROE: 14.04% (average about 157 stocks)
Top 10% by ROE, quarterly list reconstition but annual rebalancing to equal weight, after 0.4% round trip trading costs: 13.85%
Ditto, with 20% long term cap gains tax and 40% short term cap gains tax: 11.78%

The expectation is that if you pick a biggish dartboard set from any of those groups, you'll get a pretty close approximation of the return of the whole set.
The deviation will be reasonably small, and is as likely to be to the upside as the downside.

Is yearly (or 6 months or 2 year or quarterly) rebalancing an integral part of the strategy of can one mere let it run. This could potentially capture an inevitable multibagger while rebalancing could capture "sell high buy low"
It's a "Moneyball" thing. You're not trying for home runs, you're just trying for a slightly above average number of on-base hits.
Besides, things that just had a REALLY good year rarely have another one or two really good years right after.
It happens, but it's rare and unpredictable.
Consequently a cyclically repeated rebalancing will be trimming short term winners and buying short term losers, so you do pump a little profit out of random noise.

But perhaps the main purpose of rebalancing is to make sure the things you own are still members of your original eligibility list.
They aren't bankrupt, they aren't delisted due to missing statements or a penny stock price, they haven't been bought out by an unsuitable firm, etc.
And you aren't just holding cash for some position because a holding was bought out a while back.
I have done lots of testing with quarterly and annual portfolio reconstruction, with rebalancing to equal positions either quarterly or annually.
Those work fine.
You can also go "quarterly, but hold a minimum of a year" if that helps your tax situation, which I gather is the case for US Persons.
Note, several brokers have one-button rebalancing commands now, including Interactive Brokers.

How could one incorporate DCA into the strategy. As I am in working age, with frequent contributions, could one just buy a new random stock with new money?
Well, you're probably want to start with enough stocks that your portfolio is statistically going to resemble the target group passably well. 30?
But after that, sure, you could add one new stock
I would lean towards each purchase being 1/N of the portfolio value, where N is the number of positions you are about to have.
Of course, once you own all the eligible firms, you'd have to sell something.

But personally, assuming your initial portoflio has the target number of positions, I'd use the broker rebalance button and always have the same number of positions.
Commissions are low and it's really easy these days. Simpler in several small ways.

Jim