And replication studies are very difficult to get published, let alone funded.

That's why commercialization is a better metric than replication. If nobody is willing to pay for it, why should my taxes fill the gap?

There's no shortage of dodgy science in commerce.

Perhaps, but a sizable cohort of people that paid their hard earned cash for a product and go on the recommend others do the same is much more reliable a signal than an academic convincing their buddy in some government agency to allocate them more taxpayer dollars.

It took a few millenia from discovery to commercialize such things as number theory, electricity and the wheel.

And nobody's tax dollars paid for their development. What's your point?

Number theory and electricity development was/is very much paid from public funds, even dollars. For wheel there obviously was no money at all, let alone dollars.

For most science there is no obvious commercialization at least in any predictable timeframes. When there is, it's typically called R&D.

A distinction should be made between public funds from specific agencies with specific engineering goals in mind (department of energy, department of national security, NIST, etc. etc. etc.), vs "science is good we need science, health is good we need health, tell your local bureaucrat buddy how you will use science to fix health and collect your paycheck" funding (NSF, NIH).