How safe is the 4% rule if U.S. returns trend towards World returns?

Not safe at all. A 4% withdrawal rate would require the US stock market in the 21st century to produce returns similar to those of the 20th century, i.e. in the vicinity of 7% in real (inflation-adjusted) terms. Fair estimates for stock returns going forward are not this high. Rick Ferri proposed a real 5% over a 30-year horizon in 2015. I recall Bernstein in his book "Rational Expectations" (2014) proposing a real 3.6% over the very long term. These long-term estimates are based on the Gordon equation. According to this model, the long-term growth of a 100% SP500 stock investment in real terms would be the current dividend yield (~2%) plus the expected per share dividend growth rate (often given as 2%).

Bernstein's opinion on this subject is as follows: "Two percent is bullet-proof, 3% is probably safe, 4% is pushing it and, at 5%, you're eating Alpo in your old age [...] If you take out 5% and you live into your 90s, there's a 50% chance you will run out of money." (Source)

It is interesting to look at what happened to other countries in the past to get an idea of what could happen to the US in the future. The following graph shows the maximum sustainable withdrawal rate by percentage of allocation to stocks for various countries. The graph shows that despite the popularity of the "4% rule", very few countries could sustain a 4% withdrawal rate between 1900 and 2008 (before the crash) regardless of the stock/bond allocation. Even in those few countries, mainly the US and Canada, where it could work reliably, allocation mattered: At 100% stocks no country sustained a 4% withdrawal rate for every 30-year period in the 108 years of the data. Take a country that was not devastated by war in the 20th century like Switzerland or Australia. With a 100% stock allocation, 3% would have been too much for Switzerland but ok for Australia. With a 50/50 stock/bond allocation, 3.5% would have been too much for both countries.

It seems likely that the 21st-century US will do less well than the 20th-century US in terms of maximum sustainable withdrawal rates, given expected stock returns. Notice that except for Spain the countries that at some point failed to support a 2% withdrawal rate were all devasted by WW2. Spain had a civil war in 1936.

Image source: https://www.bogleheads.org/wiki/Trinity_study_update

EDIT: @DavePhD asks: If your calculations involve "a 30-year retirement duration", then can't I stick all my money under the matress and use 3.3% percent of the original amount each year, or at least get 0% TIPS [inflation-indexed bonds] and spend a real 3.3% of the original amount a year?

Answer: The mattress strategy, with 2% constant inflation and a 3.33% yearly withdrawal adjusted for inflation of the original amount, will bring you to the end of year 23 and a 2.5% withdrawal rate, to the end of year 29. If you take 3.33% of the original amount out every year without adjusting for inflation, you will have to spend almost half in real terms in year 30 as you did in year 1, which is unacceptable for most people.

The TIPS strategy would work as you describe, assuming that:

1. You build a TIPS ladder, with TIPS of different maturities. This means that, if you retire in 2020, you could arrange for 1/30th of your TIPS to mature in 2021, 1/30th in 2022, and so on until 2050. None of this will work if you sell the bonds before they mature, because then you would expose yourself to changes in interest rates. (If rates go up, the value of your bond falls and you will make a loss if you sell, but not if you hold to maturity). By extension, this method will not work with TIPS ETFs. You have to hold the securities yourself and arrange the expected payments (both interest payments and principal repayments) so that you do not have to ever sell the TIPS.
2. The real yield is non-negative on purchase (or else you'll have to satisfy yourself with less than 3.33% of the starting amount each year).
3. Either a) It is invested in a tax-sheltered account, or b) The after-tax yield is non-negative
4. The issuing authority, the US treasury in this case, does not default
5. You die on schedule after 30 years.

Point (5) is important. Note that the graph above shows you the maximum withdrawal that always worked for a 30-year period in the past for a given allocation of stocks and bonds. This means that at these maximum withdrawal rates, with 1% of the starting retirement years you would have gotten exactly 30 years of withdrawals. But with the other 99% of the starting years, you would have gotten more years than this, giving you a buffer in case you lived more than 30 years in retirement. With TIPS and 3.33% withdrawals, you have no such buffer, if you don't die before the end of year 30, you will run out of money.