Of course they would, it would be the most valueable item on the planet (asuming there is an internet surrounding it). You could charge millions for todays 65" OLED TVs in 1980. The price for polio vaccine in 1920? Well, no billionaire would risk any of their offspring to suffer from polio.

We literally have billionaires flying to space and longing for other planets today - way more useless than a smartphone.

Why would an internet that only the billionaire is on be worth anything?

It is a hypothetical that you chose to not want to understand. Replace phone or flatscreen TV with something more available, such as a modern midrange car - gasoline/diesel and streets were widely available in 1920.

Or the option to cross the atlantic in a day instead of 3 weeks. Etc.

The whole point is, basically everything that is widely available to the broad population today wasn't even available to the ultra wealthy back then, let alone the broad population. People just take this stuff for granted nowadays.

Right which is fine. Where it veers of into absurdity is when people try and claim we are better off then the ultra wealthy of yesteryear because we have access to cellphones or transatlantic flights.