If the stock is trading at true fair value, these two effects precisely cancel out and there is no change in value per share. (the amount of value per share coming from earnings rises, and the amount of value coming from spare cash falls the same amount).
...
Only at the very instant of the share buyback. After that, they don't cancel each other out anymore.

Not so.

Any given stock has one true actual value, which takes into account all of its future growth and discounts it perfectly back to the present. Of course there is the minor disadvantage that you never know exactly what that number might be : ) ...but let's posit that there is such a number.

At that number, the "true value" of my example, the cash is worth exactly as much as the shares for which it is exchange, and there is no value gain, no matter how quickly (or slowly) the business grows after that, since that was taken into account in assessing the true fair value.

So, you have to separate the two problems. Estimating true value, and whether a buyback is a good idea or not. If you merely assume that the first problem has an answer, then the answer to the second one is obvious: any purchase above that value destroys value for a continuing share, and any purchase below that value adds value to a continuing share, without exception. It doesn't matter if the company will be worth a trillion or zero in a few years, that's all part of question 1, not question 2.

There are two oddities to bear in mind.

First, the "One True Value" itself of a share depends on how willing management is to do lots of buybacks. If it's a firm that does buybacks only at deep discounts to true value, it's a good firm and true value is higher. If it's a firm that does buybacks at all kinds of valuation levels, it's a worse run firm and the true value of a share is lower. The more the buybacks are a good idea, the more they're a bad idea!

The second oddity is that destroying value with a buyback done at a price above true value can sometimes be the best available idea: maybe it destroys less value than the alternatives that might take place, like ill-advised M&A. For a firm with cash considerably beyond foreseeable capital deployment opportunities, a buyback at (say) 5% above true fair value is probably better for the true value of a continuing share, for the weighed average shareholder, than paying that same amount out as a special dividend.

Jim