There’s a relevant joke:

Two people on a hike see an obviously hungry mountain lion in the distance running towards them. One of them quickly starts changing his hiking shoes to running shoes; to which the other responds “do you really think these shoes will let you outrun the mountain lion?” To which the first responds: “I don’t need to outrun the mountain lion, I only need to outrun you”

Whether it’s 1ms or 1s makes no difference; for a class of strategies, any time advantage can tilt the average from “unprofitable” to “profitable” when you are faster than others - and the sums changing hands are huge (trillions notional or even thousands of trillions per day). A tiny advantage easily translates into a lot of money.

The people who bored the hole were paid a wage that allowed them to support their families. The company that made the boring machine received more capital to develop better machines. The company that made the fiber employed thousands of workers and engineers who are advancing the state of material science. The engineers who built the optics are furthering our ability to drive down the cost high speed data transmission. The provider operating the circuit is paying hundreds of employees and engineers who build out new infrastructure for other customers, universities, businesses. The HFT firm can now build a datacenter outside of the metro, freeing up land to house residents in the city. Banks can take advantage of the liquidity to reduce transaction risk and offer lower rates on financial products to customers. Customers who spend less on loans and credit have more money to spend on other things.

This process goes on, and on, and on. It’s why capitalism is so effective as an economic system. And also the reason why things that may not seem like they produce value actually produce extraordinary value for society.

By that argument, any kind of "make work", doing something pointless, provides value to society as a side effect.

For example: Consider a job going to the office to write on pieces of paper and then throw those pieces of paper into the incinerator so nobody will ever read what was written.

Sounds pointless. Is it "providing value"?

By your argument yes: All those people were paid and can now support their families. The paper makers made paper and advanced the state of the art in fine paper-making, as did the pen makers and the ink makers. The incinerator is looked after, and it keeps new incinerator designers in work. All the fuel which is mined to run the incinerator keeps miners busy. All the commuting to the office and back keeps train operators busy.

And yet, going to the office to write things on paper and then destroy them repeatedly does seem rather pointless.

It doesn't. These kinds of actions are entirely competition between HFT firms (the fastest ones get the biggest share of the pie). But the HFT firms as a whole do provide a service to the market, and at a much lower price than the alternatives, even with the apparently extravagent cost of these efforts (mainly because it requires a lot less people: old-school market making involved a lot of people on trading floors).