I think you need to justify the "needless" in your description of such back-and-forth speculative trading, as it a) has gone unquestioned b) is not self-evident, and c) otherwise begs the question about whether we need to actually do anything about it at all.

Seems generally correct at the first sight, but to be more sure about it, I would like to read an analysis by an economist who is able to consider more side effects than I am aware of.

The specific impact on society could also depend on many small details, like how exactly is the tax specified, what exceptions are there, how exactly the tax must be documented and paid, in international business how is it decided which government will get the tax, etc.

For example if A must pay 1% tax when selling something to B, and then B must pay 1% tax when selling the same thing to C, would it be possible to create some arbitrage system that would convert it to only one transaction from A to C, thus avoiding paying half of the tax? What if people only did business with virtual dollars, and once in a month converted those virtual dollars to the real dollars, paying the 1% tax only for real dollars that change hands? Would such system allow to replicate the current nanosecond stock trading, making this tax mostly meaningless?

On the hand, if the law would tax every virtual currency, it could end with World of Warcraft players having to include every XP gained for killing a murloc into their tax report. Perhaps a tax expert would be required to estimate the value of LW karma in dollars, too.

Wow, sorry about the stupid autocorrects above.

As have been pointed out on e.g marginalrevolution.com, one reason HFT is so popular is because the minimum stock price increment is one cent. HFT might conceivably lose much of its allure if this lower bound is changed to, say, .01 cent.

I'm not convinced trading must be intelligent to provide beneficial information to the market. I'm also not convinced all HFT systems have identical systematic errors. Can you give some examples?