With all the discussion of the costs and benefits of allowing women to vote, it's natural to ask the next question: why do we need democracy at all? If society could be more prosperous had women not been allowed to vote, then perhaps they shouldn't have been allowed to do so. The problem then, however, becomes a question of who gets to set the goals, and who gets to define "prosperous" (since we're not merely talking about monetary prosperity, but utility, and utility is different for everyone).
Historically, the people who have gotten to define "prosperous" have been people with hard power. Hard power represents the ability to use physical force to compel others to conform to your desires, and is often manifested in the form of armies and weapons, real estate and capital, and the knowledge and desire required to apply these tools to disagreeable circumstances. America wasn't able to break free from England purely by the virtue of our natural rights to freedom and liberty; rather, these rights and our desire to possess them motivated our forefathers to use their hard power to overthrow English rule. It's often said that we "have" a right to this or that, but unless we have the hard power available to seize and defend that right, it's little more than a rhetorical construct.
God may grant us the rights of life, liberty, and the pursuit of happiness, but unless we have the hardware to back it up we're likely to have those rights taken away in fact. Our natural rights are not rights that are enforced by God, but they define the extent to which it is permissible to use force against each other, and they define who is right and who is wrong in such conflicts. If you attack me without provocation, God is not likely to intervene to stop you -- but he will sanction my use of hard power in self-defense. (SDB writes a little about hard power as it applies to relations between countries.)
The power to vote is not hard power, but soft power; votes only have meaning as long as those with the hard power respect them. If you look around the world, internationalists want to replace the hard power of armies with the soft power of UN negotiations, international courts (ICC), environmental treaties (Kyoto); however, dictators and strongmen continue to subjugate their people through the use of hard power, and generally show no respect for soft power unless it happens to coincide with their wishes -- take Saddam's treatment of the myriad UN resolutions, for example. Soft power can only be used successfully when those who possess hard power restrain themselves.
As I wrote in part 2, above, voting is not a right; as such, if you are forbidden the power to vote you are not being inherently wronged, as long as your true rights are not being violated. Using force merely to gain the power to vote is not morally acceptable. However, it's uncommon for societies with a single voter (a king), or a small, select group of voters (feudalism, or an oligarchy) to respect the rights of those without hard power of their own.
This situation sets up a rather interesting conflict, assuming those with hard power want to respect the natural rights of those without. Those with hard power can set up social institutions (democracy, courts, &c.) to ensure that everyone's natural rights are protected, but if those soft power structures overstep their bounds they will become burdensome, and they may eventually be overthrown. This perspective views democracy and other forms of soft power as grants from those with hard power who have an interest in respecting the rights of the powerless.
Soft power structures show their true strength over time, as they manipulate the foundations of hard power. For example, the 2nd and 3rd Amendments attempt to permanently diffuse the concentration of hard power, on the basis of the natural rights to private property and self-defense. These words don't factually eliminate the hard power that could oppress you, but over time they work in the minds of men to change their thoughts, and to further ingrain the respect for you rights that led those with power to restrain themselves in the first place. Soft power must entice and coerce hard power, subtly influencing over time.
Democracy has proven to be quite adept at manipulating and controlling those with hard power. America's military is the most powerful force that has ever existed on the planet, and if its generals were able to wield that power at their own discretion they would rule the world. But America's military is under civilian control, and that control is passed on every few years without involving the use of hard power. This principle is not merely written in our Constitution, but is ingrained in the hearts and minds of every man and woman who carries a rifle or drives a tank. They possess hard power, but they restrain its use because of their committment to the powerless.
Was our initial government in 1788, after the ratification of the Constitution, democratic? Yes, although only a limited group of people was allowed to vote. Under our modern system, many more people are allowed to vote, but still not everyone: children, convicts, non-citizens, the insane, the unborn(?). Are we democratic? Certainly. There is clearly a range of suffrage that is allowable under democratic rule, and over time we have moved along that spectrum -- but I don't expect that we will ever move to total suffrage, because those with power (hard and soft) don't think that granting the power to vote to those without it would lead to a better government.
Do children, convicts, non-citizens, the insane, and the unborn have the rights to life, libery, and the pursuit of happiness? Each of those groups of people has their power limited for different reasons, and many would argue that some have rights and others do not, for whatever reason. At the root level, however, the question of granting soft power to these groups comes down to that of the interests of those who currently wield power. And we say no. We may or may not recognize and respect their rights (if they exist, which is a separate issue), but we don't grant them power because we don't think it would be in our best interests They do not possess hard power of their own to use in seizing soft power.
Our nation is free and prosperous as a direct result of our respect for each other's natural rights. Economic liberty and social freedom have given us a tremendous amount of hard and soft power, and we use that power to create wealth and raise our standard of living, as well as to (hopefully) spread the values that have led to our success. Our experience has shown that rights are more likely to be respected when power is diffused as widely as possible. In response to part 1, a commenter wrote that by recognizing the rights of women (and by granting them soft power?) we have attracted the best and brightest women from around the world, and that they add immeasurably to our prosperity. Our foundational ideas hold that when rights are respected, economic and cultural success follow behind.
Making fine cultural adjustments is difficult and error-prone, as in general we decide against it. It may be the case that granting women suffrage has been a net loss, but it's so difficult to calculate -- and the gross benefits are so obvious -- that the nation (and those with power at the time) decided to err on the side of further diffusion. We do restict the power of some groups based on what most believe are rather clear criteria, but those circumstances are limited and (except for the unborn) mostly non-controversial.
So why democracy? Because democracy tends to diffuse power more successfully than any other form of government, and diffuse soft power limits the interference of those with hard power by subtly manipulating their goals and desires, thereby increasing their respect for the rights of the powerless.