He seems to be popular because he has a very simple tax plan.
And he has a very simple tax plan because it wouldn't work.
There are the obvious political objections that he'd never get something like that passed without a Republican super-majority; Democrats would block it. The plan is highly regressive, at least not without some other details in there to offset relatively higher taxes on the poor and small businesses versus much lower taxes on rich and large corporations. Not only does tax incidence matter, but also a strong utilitarian objection can be raised because of the diminishing marginal value of money as one increases their income. Taxing poor people makes much less sense than is commonly believed.
I'd prefer getting rid of corporate income taxes (and payroll taxes) rather than capital gains. Taxing income and job creation is less efficient economically than taxing growth or consumption. If you have to be insistent on getting rid of capital gains taxes, then I'd prefer a larger consumption based tax with some sort of offset or prebate (similar to the Fair Tax, but not so much), and still get rid of the corporate income tax rate. It has other economic and political problems associated with it that a consumption tax would not (much harder to game), and does not actually generate much revenue for the government relative to its public image.
Next problem. Simply having a tax plan does not offer guarantees of growth. Fair Tax advocates also make wild-eyed claims about the growth of the economy based solely upon changes in the tax code (and upon which the "revenue neutral" aspect of their claims are entirely based). Cain's plan suffers from the same problem. Lower and simpler taxes we are told inspired the Reagan era growth.... except any serious economist/historian knows that Volcker's iron grip being released on the Federal Reserve had a lot more to do with that. The lower taxes that Reagan passed in 1982 did not a jot in increasing growth, and resulted in a very large tax increase in 1983 to semi-balance the budget from the massive deficit he created by lowering taxes. After which growth began (the 1986 tax reform simplifying things was much better, but by then 4-6% GDP growth was already in progress). In today's case as then, knowledge of monetary policy and pressing for a release of deflationary or decelerating inflationary pressures (as Ben Bernanke circa 2000 did, but not Ben Bernanke circa 2010) would probably do a lot more than any President's tax plan ever will. I certainly do not object to lower and simpler taxes. I think we could axe a ton of marginal deductions (starting with the home mortgage interest one), end up with a set of lower marginal rates to offset this and still significantly increase government tax receipts as a result. That's fine with me. What concerns me is the idea that such things would create job growth or some such. Because it has little to do with it. Has more to do with having an efficient government and light touch on the economy, with minimal redistributional pressures pushing money up the income ladder rather than down (we expend massive amounts of the national treasury giving money to people who already have money, and not as commonly believed, giving it to poor people).
Further problems. I have no problem with abolishing the payroll tax. I think this is a serious drag on job creation and funds programs that I would like to see function less as entitlements and more as social safety net roles anyway (medicare and social security). But first those programmes are popular among most of the American populace not named "me", and so gutting their funding is not exactly going to go over well. Second, even if we were to magically succeed in gutting their funding even a little, that money is still going to have to come from somewhere, and nowhere in Cain's tax plan is that source of revenue described. Those entitlements are #1 and #2 on the government's expenditure list and are mostly funded by payroll taxes right now. So if you propose to abolish the taxes funding them, either you should also propose to abolish those programmes (Cain hasn't), significantly reform them and describe how they would be funded out the general revenue (Cain hasn't), or admit you are an idiot who is pandering to other idiots (appears to be the case based on other Cain statements on issues like religious freedom, civil liberties, knowledge of foreign policy, etc).
In a race largely about the economy and the deficit, Cain looks more or less like Bozo the Clown because he's not offering much on the economy (to be fair, nor is anyone else) and he's offering a way to double down on the deficit by massively decreasing tax receipts and not listing off a bunch of spending cuts to go with them.
"Starve the beast" as it was once known, does not work. Reagan increased spending, not decreased. Bush increased spending, and deficits grew under both to what were once considered massive peacetime proportions. One suspects justly that a Cain administration would be little different. I cannot in good conscience let people delude themselves into thinking it will be otherwise.