I don't believe that he wants to prevent anything, but he suggests that trades should be taxed to create some value to society from this. He is suggesting their value (at the moment) is exclusively to the benefit of making rich people - who can pay for access early information and technology - richer.
Unfortunately for your argument, our stock markets are. They wouldn't be remotely viable if they weren't supported and regulated by government. In exchange for the tax payer funded assistance is the social benefit of keeping the whole thing running.
Or would you like to test the viability of a market with no government oversight and no government enforcement of contracts?
If you want to claim an HFT shop is "quasi-governmental" because contracts are enforced, then basically every enterprise in the world is "quasi-governmental" (except for the black market).
Second, copyright enforcement and free speech have defined limitations for the betterment of society.
The corollary to that is that your trades as a mere producer are never going to be [indirectly] profitable because all potential profits from varying price have been swept up by others who're not producing goods/services but instead are only operating to extract value that would otherwise go to producers.
It's really concerning how little people itt understand about markets
Is it worth the cost?
There's no reason to believe total taxes collected will decrease. If actors still benefit from HFT post-taxation, they will still trade, and pay the tax.