Yes, we can definitely argue about tax/cost vs. liquidity - as I mentioned in another comment, we could have different exchanges encourage different levels of liquidity (resulting in different costs of trading) - investors would then be able to choose what they prefer - liquidity or lower trading costs. To avoid adverse selection, companies could even do it on a per-stock basis (or the regulator could run per-stock experiments, and analyse the effects).
I don't know the details of HFTs in general, but to my understanding, what they do is arbitrage (orthogonal to liquidity) - basically, making sure that any simple patterns in the price are exploited (and thus reduced). Note, however, that HFTs themselves don't make money - the markets could be just as efficient if only HFTs would participate, and with any new piece of information (earnings release, news, movements of other prices) a new equilibrium would establish (best bid and best ask) without any trades happening. Trading either comes from (1) disagreement about the price - and the person who's right earns money, rightfully IMO (and if you don't want to lose money, just don't play), or (2) external circumstances (e.g. you want to buy a house => you need money => you sell your stocks), in which case HFTs are actually helping you (reducing the spread, and still earning money - e.g. a "stupid market maker" offers you 100 and then sells it for 101, earning 1, whereas the "smart HFT" offers you 100.01, and then sells it for 101, earning 0.99 - and you're better off as well).
This isn't the whole story, of course - there's probably a lot of illegal things going on (dark pools, front-running, order flow selling), and a lot of waste could be reduced (e.g. by regulators forcing HFTs to share/rent infrastructure and only compete on algorithms, or mandating everyone has the same delay to the exchange), but those are problems only if you let HFTs exist.