Visible taxes can lead to bad policy choices when a tax's visible incidence is different from its actual incidence. The average tax payer will vote for a tax/benefit scheme that appears to be in his or her interests - for example, increased health care spending financed by increased corporate income taxes - not realizing that the burden of the corporate income taxes might be shifted forward onto customers or backwards onto employees - in other words, right back onto the average tax payer.It's a nice second-best argument. And, consistent with one of my favourite papers in experimental economics (previously discussed here): Sausgruber and Tyran's finding that buyers in a double-auction will happily vote for inefficient redistribution programmes framed as a tax on sellers but will oppose it when framed as a tax on buyers, despite equivalent incidence.
I'm not sure that a tax's invisibility necessarily protects against stupidity. New Zealand's clean GST is built into consumer prices; there's still not unreasonable pressure to wreck it by exempting food. But, that Labour's only advocated the wrecking ball when safely away from the Treasury benches suggests something.
A final argument for stealth taxation is that it facilitates budget balance. People want good things from their governments, like health care and old age pensions. But they don't want to pay taxes. So the temptation is to vote for spending initiatives and vote against any tax increases. When taxes become more visible, people become more aware of the taxes that they are paying, and lobby harder for tax cuts. The result: future generations are burdened with debt and taxes.
Now the argument could be made that in fact invisible taxes contribute to government debt - if the average voter realized how little he benefited from the Bush (Bush-Obama?) tax cuts, how much those tax cuts benefitted the richest Americans, and just how mind-bogglingly rich the richest Americans are, perhaps he would have voted against them. I don't know of any decisive evidence on this point, so if you disagree, feel free to say so in the comments.
Some degree of visibility in taxation is desirable - without information how the tax system works, and who bears the burden of taxation, it is difficult to make good policy decisions.This is a fun one to think through. Specify that voters are largely ignorant but will vote against anybody they think is to blame for bad outcomes. And, specify a Westminsterian system so they know who's to blame for bad outcomes. In that world, I'm not sure whether it matters a lot whether the taxes are hidden or visible. If taxes with too high of deadweight losses are used to fund services of too little value, incumbents get turfed. Maybe it takes slightly longer if policy has lagged effects. Retrospective economic voting then saves things. If there's no opacity, the ruling party has to balance losses from bad effects of policy against loss in popularity from running "works, but unpopular" policy. At least there's weight on the effects of policy despite voters not knowing a damned thing except what they see out the window.
In a political system where responsibility attribution is more difficult - either Parliamentary with PR and powerful committees or a Presidential system with strong division of power and a federalist structure - things are harder to work out and could then persist longer. Then there's rather less incentive to weigh the effects of policy; rather, you blame the President if you're Congress, blame the other party in Congress if you're the President, blame the State if you're local government. Blame gets spread and incentives for good policy are flattened.
I'm also not sure that complete opacity is as good an idea in a Brennan-Buchanan Leviathan taxation world than in a Musgrove benevolent despot one.