That is a fairly bold prediction. Given that Stanford was able to achieve so much in less than 125 years, I would say that fortunes of educational institutions can rapidly rise and fall. If the administrators of any of these Universities take their eye off the ball for a few decades, then they might find themselves playing catch up.
Also we don’t know where the next “big industry” will arise. If the focus shifts away from the Valley, then Stanford’s fortunes might follow. If the weather or any major climatic change plagues California, we may also see a decline in its popularity. Remember that CA is dependent on water from the Colorado river and if climate changes severely impacts that, we could also see a shift. And then there is the San Andreas Fault.
Another factor might be the kind of students these Universities recruit. Lets say these universities continue to expand access to education and increase the percentage of first generation kids to lets say 30 or even 40% of the incoming class and also expand access to minority and lower SES students, because their strong endowment allows them that flexibility and yet income inequality continues to grow and in fact worsens in the US, could that affect the strength of these universities in 100 years? Who knows? Too hard to tell right now. It would depend on whether success in US becomes dependent on “who you know” or on “raw talent”.
In other countries when income inequality became too great, it became very hard for folks to rise to the top from the bottom even if they went to the best schools if they didn’t have the right connections. So that might also affect the fortunes of these universities, as the next generation of alums grows.
In short I don’t think it is easy to predict these things. Too many factors.