The LEGAL reason is because it is against the law.
There are reasons which go beyond simple moral reasons. The laws of our society (laws of property ownership, inheritance, parental rights, marital property, etc.) are structured on the assumption that only two people are involved in a marriage. The legal side is just too complicated to allow bigamy. Allowing plural marriage creates situations which the law CANNOT handle.
If the man dies and still has bills and debts, who is responsible then? You would have to think of life insurance as well. When he dies does the insurance company give each wife the amount of the policy or do they divide it among them. That would probably cause a big lawsuit. I think if someone needs more than one person in their life, (sexually, spiritually.etc) they should just not get married.
Whether you want to believe it or not, America is a Representative Democracy. So if a VAST Majority of people do not like polygamy (for whatever reason--moral, religious or otherwise)--the representatives will be obligated to make and ensure it is illegal.
Also, there were too many cases during the time the law was made of young and of age girls alike, being forced by their families, citing beliefs, into polygamy, using the abuse of polygamy as a reason to have several wives, neglecting and abusing them emotionally and physically. Ideally there is nothing bad about polygamy, but this is not an ideal world. There were many times the law couldn't get the abusers of polygamy because of the control they have over their wives and the citation of religious beliefs. Therefore, the law has no choice but to ban polygamy in general because laws can't have exceptions.
Now we're in the 21st century and the abuse is still an issue. So why would the laws change now when nothing has changed? Plural marriage occurs when the women are very young, and it might reasonably be determined that exploitation and coercion are involved more often than free choice. Great Example: The recent FLDS indictments against 12 men for sexually assaulting minor girls (In the name of religion.)