A considered response that I will have to take point by point.
* It requires no more bookkeeping or accounting beyond that which is already required by the census.
That bookkeeping while annoying is extremely profitable, every additional dollar added to the IRS budget results in 4 dollars of revenue[0]. Simply put from a governmental perspective it's highly cost effective. While a head tax might be cheaper directly to implement, it has other costs that aren't considered that I will get into below.
* It would apportion federal taxes to the states in proportion to their populations, as required in the Constitution prior to the income tax amendment. This could potentially reduce the number of taxing authorities any given individual would be exposed to. Your state might pay the federal capitation, but might raise the funds for it via other methods of taxation rather than its own head tax.
I concede this point, but this more of a solution looking for a problem than anything. Moving money into different accounts is pretty much a solved problem.
* It reinforces the idea of equality before the law.
A flat percentage after a single deduction related to the cost of living would be equality (a man should not be taxed before he feeds himself in my opinion), the myth that the CEO and board actually created the billions of dollars that his corporation captured (because he worked a few hundred times harder then the guy pulling 12 hour shifts on the factory floor) is old and tired. It was his employees that did so as well, and taxing them at a far greater percentage (79.58% on minimum wage to be exact) than him is not equality. It's theft.
* It encourages pursuit of additional income. You are more likely to do additional work for an extra $500 if you then get to spend all $500 of it, rather than just 75% of that.
Firstly, Where is this a problem? On the one side of the spectrum we have the poor working 3 jobs to pay rent (whom you propose to more than quadruple the tax burden on, thus all but stopping the velocity of capitol and probably destroying the economy[1]) whom need to earn as much as they possibly can just to get by. On the other side the wealthy/upper middle class is generally obsessed with status symbols. That won't change if you tax them at 4,40, or 91% (see 1953 - 1961). They will still want to buy the newest Tesla, send their kids to whatever expensive school and go on exotic vacations as long as their neighbors do. Hell, in bad times many of them finance it up until bankruptcy to keep up appearances (see 2008 - 2010). The data is clear, they will continue to work and spend as they always have.
Secondly, Not once has someone gone, "Yeah I'd take that 10 million, but I'd have to pay 2.5 in taxes, so burdensome, forget it" and even if they did, someone else will step up and fill the void if a market exists. On the other hand if you tax a minimum wage employee at 80% why the hell would you even bother going to work? You are homeless and hungry either way, what will the few dollars you earn for 8 hours of work get you? Might as well sit in the park and panhandle, it's more profitable.
* The government is encouraged to promote increased birth rates and immigration as a means of increasing its revenue.
They aren't now? I see plenty of tax benefits for having children. More people, more consumption, more incomes, more revenue. The only difference here is the government has no incentive to raise the average rate of pay of Americans. Why educate them so they can get better jobs? Why worry about the state of the economy? They pay $1000/month anyway. A percentage doesn't have this problem.
* But the number one argument both for and against against head taxes, depending on who you are, is that it creates an inherent de facto limit on government spending, based on what the lower class can afford to pay. If there are people who simply cannot pay more than $500 a month, you cannot raise more than $500 x population via the capitation. So you can't spend more than that without resorting to other sources of revenue.
Firstly, why can't the government just take out debt like it does currently. This plan does nothing to prevent that and a proposal to do so can be applied to any tax plan (IE, constitutionally prohibit the government from taking new debt).
Secondly, I'd argue that the working poor can't afford the current levels of taxation. Raising it to above 60% for the working poor and below 1% for the wealthy is not a solution to that problem. In fact, the entire reason for the 2nd amendment is to prevent something like that from happening. If anyone seriously purposed this change there would be riots in the streets. If it passed, many would die before it was repealed or the government overthrown entirely. This is the nation that started a war with the greatest military power on earth at the time over a 3% tax on a single non-essential good, you'd be wise to not forget that. The rural poor certainly haven't.
So in conclusion, the people advocating this wish to lower their taxes at the expense of others and use justifications that make little sense in order to attempt to do so.
[0]http://www.cbpp.org/research/federal-tax/irs-funding-cuts-co...
[1]https://www.imf.org/external/pubs/cat/longres.aspx?sk=42986....