The premise of the post is incorrect if "minor" is given its usual meaning in the U.S. of under age eighteen (except in California, Idaho, and North Dakota, and for virgins who live a "caste life" in Massachusetts).
Sex with a minor is legal in the vast majority of U.S. states to some extent, although commercial sex (i.e. prostitution or trafficked sex for money) with a minor, and child pornography are illegal in the U.S. and punished routinely and severely.
The median person in the U.S. has sex for the first time at age 16 (which means that a large share of the population has sex before age 16) and prosecutions are very rare, even though many instances of statutory rape present (especially in the most strict states). The percentage of instances of minors having sex that would constitute statutory rape if the minor was not married that are not statutory rape because the minor is married is tiny.
While prosecutors can prosecute statutory rape charges in cases that the prosecutors believe are consensual and involve post-pubescent parties, they rarely do so over the objection of the alleged victim, on the theory that this does not advance justice or the well being of the alleged victim. Also, crimes that are never reported aren't prosecuted, which people who consensually engage in sex that constitutes statutory rape rarely report.
Minors can typically marry only with parental or court consent (although some states allow girls who are sixteen or older to marry), although there are exceptions.
As @DavidSiegel notes, all statutory rape laws in the U.S. expressly exempt lawfully married couples (at least for post-pubescent married people). Historically, marriage was a defense to all forms of rape charges. Now, in most U.S. states (if not all), it is a defense only to statutory rape charges.
Some context is desirable. Consider the case of New Jersey (chosen simply because I could easily find data on point; this answer contains some plagiarism, i.e. quotations of myself without express quotation marks or attribution).
In New Jersey, it is statutory rape for someone 18 or older to have sex with someone younger than 16, even if the sex is consensual.
I don't have exact statistics on statutory rape prosecutions in New Jersey, but if it is prosecuted at a similar rate to Colorado, there are less than 1000 misdemeanor rape prosecutions a year only some of which are statutory rape prosecutions (a prosecution of statutory rape involving someone old enough to marry is usually a misdemeanor).
Of course, the vast majority of cases of sex with minors involve neither marriage nor pregnancy.
There were roughly 90,000 girls in New Jersey who were aged 13-15 years old and 60,000 girls who were 16 or 17 years old, when the last census was taken in the year 2010. According to an opinion piece in the New York Times (corrected from the original erroneous version of the article):
3,481 children were married in New Jersey between 1995 and 2012. Most
were age 16 or 17 and married with parental consent, but 163 were
between ages 13 and 15, meaning a judge approved their marriages. . .
. 91 percent of the children were married to adults, often at ages or
with age differences that could have triggered statutory-rape charges,
not a marriage license.
This is about 193 children including 9 between ages 13 and 15, in an average year.
Overwhelmingly, people who marry before age 18 are girls rather than boys, and this is even more strongly the case when people marry between ages 13 and 15. So, the annual marriage rate for girls between 13 and 15 in New Jersey in the relevant time period is approximately 1 in 10,000 (i.e. 0.01%). In truth, there are probably significantly more 15 year olds than 14 years olds, and significantly more 14 year olds than 13 year olds in that sample.
The odds that a New Jersey girl will marry any time in her life before age 16 is about 0.03%.
The annual marriage rate for girls aged 16 and 17 in New Jersey in the relevant time period is about 1 in 326 (i.e. 0.3%).
The odds that a New Jersey girl will marry before turning 18 in New Jersey is about 0.63% (i.e. about 1 in 159). The other 99.37% of New Jersey girls will not marry before age 18, although many who do not marry will have children.
There were about 1,030 children born to mothers aged 15 to 17 in New Jersey in 2014 (a rate of 5.8 per 1,000 girls aged 15-17 down 15% from 2013 and down 78% from a peak in 1991), and about 37 children born to mothers under age 15 in New Jersey in 2014. Thus, there were 1,067 children born to mothers under age 18 in New Jersey in 2014 and roughly 193 marriages of girls under the age of eighteen.
Black and Hispanic girls are roughly six times as likely to be mothers under age eighteen as white girls in New Jersey.
There are about 5.5 teen births by mothers under the age of 18 in New Jersey for every marriage by a girl under the age of 18 in New Jersey (8% of the births by teens under the age of eighteen are second or later births). About 94% of births to mothers aged 15 to 19 in New Jersey are non-marital. So, there were fewer than 64 births each year in New Jersey to married mothers under the age of eighteen in 2014. Indeed, the number is probably significantly less because if 15-17 year old mothers were equally likely to be married as 18-19 year old mothers in New Jersey, the number of married teen 15-17 year old mothers would be 18 in 2014, and in fact, it is almost surely the case that 18-19 year old mothers in New Jersey are at least somewhat more likely to be married than 15-17 year old mothers in New Jersey.
The rate at which teens under the age of eighteen become pregnant in New Jersey is roughly 8 times the number of births to teens under the age of eighteen in New Jersey. Some of that is the statistical quirk the arises because more than three-quarters of seventeen year olds who get pregnant ultimately give birth when they are eighteen. But, probably something like a third of those pregnancies of girls under eighteen years of age end in miscarriage or stillbirth, and roughly half of those pregnancies are terminated with abortions.
The facts suggest a couple of things.
First, the nearly 80% decline in births to mothers under eighteen since 1991 in New Jersey has probably been accompanied by a similarly great decline in the number of marriages by women under the age of eighteen in New Jersey since then. So, there were probably far fewer than 193 teens under the age of eighteen and were probably fewer than 9 teens under the age of sixteen married in 2014 in New Jersey.
Second, it suggests that most teenaged girls under eighteen who marry with judicial or parental consent in New Jersey, rather than being pregnant, are already mothers of the husband's children by the time that they marry in most cases. This is almost always the case when judicial consent to marriage of a girl (it is almost always a girl) under the age of sixteen is given, and there is additional screening from domestic abuse in judicial consent cases, often by a court appointed social worker or guardian ad litem.
If you are already a mother, being married give you more legal rights vis-a-vis your partner, than not being married (e.g. property division and alimony and a presumption of paternity for future births without having to prove it), and in the U.S. unlike lots of jurisdictions where child marriage is a problem, "no fault" divorce is widely available. So, the presumption that a minor who gets married is worse off than a minor who does not get married in the U.S. is mostly wrong.
Statutory rape prosecutions in these cases, which leave the teen mother and her children without a source of economic support and with a father-coparent who is less employable due to a criminal conviction for a sex offense are often not in the mother and children's interest.
Cases of minors de facto forced into marriage with much older men, while they are not pregnant from a relationship entered into without parental sanction are extremely rare in the U.S. and when they happen in the U.S. they often promptly end in divorce. This is very different from non-U.S. practice where divorce is often extreme difficult and girls who married as minors have often not initiated the relationships and may not be free to say no to those relationships.
In India, in contrast, where forced child marriage is a serious problem, such forced child marriages are declared void, and the husbands are denied the immunity from criminal liability for statutory rape that would otherwise apply.