Counter-counter point: It's not really used in branding either by any of the child companies. So they don't need it.

They have google.com, which is the brand they use towards customers. The Alphabet brand is little more than a stock ticker.

Who ever has alphabet.com will be able to sell it for 7 figures anyway, which is the point.

They use abc.xyz though, which is fun at least.

They have abc.xyz