Trading is probably essential, it definitely is given our economic system which involves trading. In my opinion, HFT does easily merit singling out for evaluation. It is a relatively marginal economic activity, but accounts for a large portion of transactions, mostly in highly liquid markets purposely designed/evolved to be highly efficient like stock markets and other tradable securities markets. I don't think pure theory economics can say much about what happens at extremes like that. Transactions are prices and information. If most transactions are based on HFT strategies divorced from anything even remotely related to an understanding of the underlying asset, who knows what wheels fall off the theoretical model and/or reality. It's worth looking at, at least.
As I said though, I agree with you that there's an onus on those proposing a HFT tax to convict it convincingly. I don't think this has happened yet. The argument can't be "weird and scary." I don't see the liquidity defense. How can liquidity beyond a certain point be meaningfully more useful, but that's not a conviction. In my mind, it rests on how HFT impacts economic fragility, and increases the likelihood or impact of busts.
We're talking about something like a 0.02% of equity tax on HFT specifically or lower if it's going to be everyone. That does not impede the ability to price in real information.
An artificial restriction on trading is not unlike natural ones. Did we have liquidity issues when trading in and out multiple times within tenths of seconds was impossible? I don't think the cost is high. The risk is ..unproven.