you haven't said anything new here. Price must rise to account for destruction of a share, but market cap stays the same... (price / share goes up, price / fraction of company stays the same)
by this logic a reverse stock split would increase the market cap. No need to even waste money buying back any shares... free market cap rise, bonuses for ceo, cfo, existing shareholders rejoice :)
What does reverse stock split have to do with it ? Buyback happens on the market and it removes stocks from circulation, if the demand is still there but buyback eliminated supply because people are holding on to the rest of the stock then the price automatically goes up and increases the market cap more - it's about liquidity - if you do a buyback of 1 billion suddenly there's 1 billion on the sell side that's gone but people still want to buy the stock - so the price goes up.
the price changes immediately when buybacks are announced, not when the buybacks are executed. Case in point, intel jumped 4% today immediately after announcing a stock purchase of $10 billion (to be executed by end of the year), which is about 5% of its marketcap. No shares needed to change hands, the bid / ask moved instantaneously. The quoted price of a stock reflects people's willingness to buy and sell at certain prices (bid / ask), its not simply the last traded price, which is almost useless, given new information.
Your logic is flawed in that shares aren't simply "destroyed" they have to be bought back on the open market at an agreed upon price from a willing seller. The sellers of the shares may not want to sell and will therefore require more than the perfect price 𐤃X that accounts for adjustment of market cap based on reduction in shares.
In theory if no one wants to sell shares of Apple during a buyback the share price will head towards infinity. There's always a price though that someone will let go of a share at.
