"The faster the price discovery, the shorter the validity time. This means a more accurate price."

A continuous market price is an illusion; let's not forget that. Every market is made up of trades, which are discrete, and every price has an unstated amount of uncertainty, which may be large by any standards. You can't know from first principles whether a change in quoted price is even a change in the market, because it could be within the +/- range that's implicit. Apple is quoted to the nearest penny, at least, but the idea that the current price is accurate to within 0.004% is ridiculous.

Edit:

"Fischer Black famously defined an efficient market as “one in which price is within a factor of 2 of value, i.e., the price is more than half of value and less than twice value,”

...I hadn't heard this before Matt Levine mentioned it, but I was like "yeah, obviously, why haven't most people gotten the message?"

But: "BNP Paribas...said [Saudi] Aramco was worth exactly $1.424394 trillion."

I wonder which particular millisecond that held for.

Edit Edit: The market has a whole (mostly) unseen dimension other than uncertainty, which is depth. You can only buy or sell so many shares at the instantaneous market price. Further away, there may be orders, but the price of the whole company is going to be way outside of that. The shorter the timescale, the shallower the "market" so you can't just say we're making progress by doing things faster. It's like when research lasers are said to make unbelievable power, but it's like for a femtosecond or something. Liquidity, in my mind, requires depth, just as with water.

That would be totally boring trading and unremarkable, but that isn't what HFT firms are doing. If that were the strategy then exchanges would presumably just sell a skip-the-queue service when two traders offer the same price and there wouldn't be much point worrying about how far machines are from the exchange.

HFT trading isn't about executing the same trade as someone else but a tiny margin faster. That wouldn't have any special impact on market spreads or liquidity, for example.

There aren't any complaints against the T in HFT; as traders they are helpful. The value questions are about the HF and whether it is a desirable part of the market or an unhelpful arbitrage opportunity created only by implementation details of the exchange.