So, one really easy way to beat the S&P 500:
(1) own the stocks directly, not via an index fund. Lots of brokerages have a one-click buy command if you upload a list.
(2) for your list of stocks to own, just use a list that is at least a year out of date. Done!
...
1. Has this technique been backtested? What are the numbers? (When I was younger, I would have stayed up all night, or two or three, and do it myself, but I'm too old for that, and I assume someone else has already done it)
2. From a US tax point of view, this could potentially become very tax inefficient. If you buy an S&P500 fund or ETF, the only taxes you may owe are on capital gain distributions, but most such funds try to run efficiently internally to avoid excessive amounts of it.
3. From any tax point of view, it could make a tax return quite a bit more complicated. I assume that in addition to adding/subtracting companies, there would also have to be substantial rebalancing which could cause many transactions in some years.
4. If this is so good and so easy to do, why hasn't anyone created an ETF or regular fund to do so?

1. Yes. The average return of those promoted and those ejected, relative to the index in the year after the change, is well studied. It's not hard to estimate the impact of that on an overall portfolio. Plus, some direct studies. Summary of the studies from Claude:
Arnott, Brightman, Kalesnik and Wu, “Earning Alpha by Avoiding the Index Rebalancing Crowd” (Financial Analysts Journal, 2023; SSRN working paper 2022). They simulate exactly the “lazy” replication you describe. The lazy-replicated S&P 500, delayed by 3 months and 12 months, outperforms the replicated S&P 500 by 13 bps and 23 bps, respectively. The earlier 2018 paper (“Buy High and Sell Low with Index Funds!”) got essentially the same figure on 1989–2017 data: implementing the additions and deletions to the S&P 500 with a delay of 12 months would have outpaced the S&P 500 by 25 bps a year.
Note, you would be paying some commissions on your individual trades, but you would also be saving a few basis points of fees.

2. It shouldn't matter for tax purposes, pretty much the same as a mutual fund index tracker, if you're doing a cap weight index simulation. The whole point of a cap weight index fund (yours or theirs) is to avoid the vast majority of trading (not, it should be noted, to maximize returns). The annual index turnover isn't altered by lagging the membership test...it's around 2%/year. I'm personally a fan of equal weight instead, but that isn't necessary if all you want is an "index tracker" that beats the index by a bit.
3. Well, I suppose. You would be selling maybe 20-25 positions per year. I think most brokerages export things you can import directly to a personal tax program, so it's hardly insurmountable.
4. My assumption: no market demand. This strategy would not track the index perfectly. It would outperform on average, and underperform some fraction of the time, but the performance doesn't matter: the market for index funds seeks perfect index tracking, not high returns. An "index fund" with tracking error would have no takers. If you're going to diverge from the index, from an investment point of view you would do things beyond merely this hack, and from a business point of view you would never call it an index fund.
There is a long line of elaborations in the general subject of "smart alpha" indexing, which eventually turns into a slippery slope, but the first "additional" thing you'd do is hold onto ejected firms for even longer. During 1990-2022, deletions outperformed the index by more than 5% per year for the next five years. That causes the bulk of the advantage, less so delaying buying the new additions. NIXT is a fund that holds onto demoted stocks, but it becomes a more complicated small cap fund because the deletions are, more or less by definition, small.

There are, of course, many funds out there that are similarly "smart alpha", using some small simple formula to reweight the index to get a bit of an edge. It's merely that there aren't any that hew to the index this closely but are in fact different.

Note, the effect is strongest in choppy or reversing markets, not in long strong bull markets. It's a long haul thing, not something that will give an edge every year.

Jim