But I can't really see why Berkshire's policy should ever be like Apple's, where shares are repurchased with the same enthusiasm at 30 times earnings as they were at 8 times earnings, with no consideration of their value or of other alternative uses of capital. If Berkshire's new management were to ever adopt a policy of paying dividends and repurchasing shares all the time in the same proportions, I would seriously question whether Buffett had succeeded in arranging for a succession where his value orientation was maintained.

It's a perfect example of the circularity of the problem.
Buybacks make sense because Berkshire's prospects for value growth per year are more certain and slightly better than average.
But if they were silly enough to keep buying their own shares at stupidly high valuation levels, that would show they had lost the plot on capital allocation, and the shares weren't worth as much, so almost any buybacks would be unlikely to be a great use of capital.

At the scale of Berkshire these days, the opportunities for big wins from a few smart big investments are over, or nearly so.
Measured by impact on Berkshire's share value, maybe BNSF was the last-ever big win on the whole-company acquisition front, and maybe Apple will end up being the last big win on the public stock front.
Instead, the continuation of increasing value at an above average rate will likely rely more and more on simply avoiding the dumb things: prudent, rather than genius, capital allocation.
It's amazing how much better one can do by simply eliminating a few big losers from the barrel.
It's not actually that hard, with some discipline: Most big losers lose because of a risk that might have been unlikely, but whose possibility was pretty foreseeable well in advance.
Common categories of dumb moves: being impatient to deploy capital (even if it's a below-usual fraction of the assets), investing in businesses that won't last long enough to earn back their prices, and buying stories that are plain overvalued.

Berkshire's style, in short: Don't speculate, don't buy something just because it's growing rapidly, just buy streams of earnings.
Aim for the most future earnings for your dollar, with the highest certainty, and the longest probable time horizon.
Reinvest those earnings the same way.
If it isn't making 7% of the purchase price now, it has to make more than 7% of the purchase price next year. (paraphrased quote from Mr Buffett)

Jim