Felix Salmon says the amazing explosion of high-frequency trading has turned him into a convert to the cause of a financial transactions tax: "The potential cost is huge; the short-term benefits are minuscule. Let’s give [high-frequency trading] the funeral it deserves."
In terms of high-frequency trading, I basically agree. Suppose it were only possible to make one trade per month. The cost there in terms of illiquidity and persisting pricing inefficiencies would be clear, and I don't really see what the benefit would be. But as you scale down to once a week, once a day, once an hour, once a minute, and once a second the calculus shifts. The marginal benefit of a little bit more liquidity or price efficiency is quite low, while the cost in terms of "crazy computer blowup ruins everything" is very high. (Just look at what happened to the Gotham Stock Exchange!)
That said, if we're out to reduce high-frequency trading, why not just implement an arbitrary cap on the frequency of trading?
A financial transaction tax has some other kinds of appeal (it would raise revenue) and some other downsides (in terms of serious questions about how you'd design it so as to actually work rather than just pushing transactions offshore), whereas a simple quantitative limit on frequency seems pretty easy to design. What's more, while an financial transactions tax would at the margin deter all kinds of traders, I bet a limit on frequency would make a market more appealing to lots of players. As long as high-frequency trading is a thing, pouring resources into developing the relevant computer technology is something lots of firms are going to do. But it's very much a red queen's race in which nobody stands a good chance of gaining systematic advantage over anyone else.