Dave and his guests made a critical error in describing their vacuum tube futures: many innovations were only possible because we developed digital computers to aid in their design or manufacture.

Without digital computers, many developments would not have been possible or would have very delayed development. We would not be a few decades behind where we are. We'd be centuries behind and very different from where we are now. The effects would be everywhere, but the financial sector would be highly affected as it would would not allow for HFT (High Frequency Trading), at home trading, debit/credit cards as we know them today or the entire crypto market. Their predictions are essentially all wrong and for the wrong reasons to boot.

TL;DR: the future would be entirely different without transistors and digital computing

I remember going to some store with Daddy and a few tubes for him to test. It was a pretty common thing 'back in the day.'

We still use some. X-Ray tubes, Klystrons, Magnetrons, TWaT tubes, etc.

They've just entered specialty instead of commonality. However there are plenty of common tubes still made, plus Korg's thing...

Interesting thought experiment. You'll need to define what a tube is. There are micro tubes and field‑emission cathodes. The tech didn't go away, it's now evolved.

Isn't that the premise of Fallout?