The first thing that would happen in such a case is that there would be a huge amount of mathematical and legal research into how to game this system too.
We could see HFT setup hundreds of legal shell entities that trade with each other on their own "internal" network all controlled by the same computer system, so the people doing the buying and selling are no longer the same legal entity. Possibly involving some form of legal futures derivative, so you are now technically trading something different, but designed in such a way that the price is set now, but the actual bookkeeping and "money transaction" is delayed for a year to avoid the tax, counterbalanced by a 0% interest "loan" repayable in full in exactly one year.
Alternatively, for frequently traded stocks, there may be the creation of pools of "buffer stock". I have buy 100 shares in X, add this to my existing pool of 1000 shares, then a half a second later sell the "oldest" stocks from the pool, which would attract a lower tax rate than selling the "newest" stocks in the pool.
The name of the game is information warfare, things are only worth what everybody else believes they are worth, you make more money if you can correctly second guess the actions and beliefs of the other participants in the market faster than anybody else. Its game theory, if you can predict what the other side is going to do, then its much easier to pick a winning move.
If we as a society use "money" to determine "value", and this is an area of the economy where more money can be made in the shortest period of time compared to any other sector, then the effect is that we allocate our best and brightest minds to solve this mission-critical problem that financially we have deemed to be the most important problem our generation has ever faced. Financially it is more important than getting man to the moon. If this sounds silly, then you have to realize that this is the exact logic behind the invisible hand of the free market and the methodology the capitalist system uses to allocate the resources (both people and things) within our society.
Given that such a high quantity of society IQ points (our top lawyers, mathematicians, economists, computer programmers) are going to be working full time at finding any and every loophole in any "simple" system designed by our politicians (who are elected based on popular vote), the danger is that any such rule would simply serve to penalise small actors in the system how are now forced to follow the new rules, yet allow the hardcore HTFs to effectively continue with "business are usual" once they have a figured out a way to circumvent the wording of the law.
So while I agree that HFT is having a significant impact on the market, and distorting it, the problem of how to change the rules of the system, such that everybody "plays fair" (which economically is a losing strategy)... it is far from simple.
Nobel Prize winner James Tobin suggested the Tobin tax, which is a tiny fractional percentage tax on all currency transactions, to help stablize the currency markets. Depending on the specifics of the market, 0.00006% tax may be feasible on the USD-EUR market. But this is still subject to markets "off-shoring" to avoid the tax, the exact long term effects of such a tax on the market, how exactly such tax rates would be calculated (too high and it affects the "normal" market, too low and it has little effect of HTF) plus the political question of who/what/where does the collected tax get spent on has yet to be solved.