As pohnpei says, it's essential for every country to maintain control of the flow of goods and people across its borders, but for the United States, there is an even more pressing reason as well. The United States is a target for terror groups around the world, and has been attacked repeatedly, even before 9/11. Most of the people who cross our borders do so for travel or economic opportunity, but some people cross it in order to do us harm. As a nation, it is reasonable and just to protect ourselves against these threats at our borders.
The major reason the US should impose immigration laws is because every country must. A country must at the very least know if people who are trying to enter the country are criminals, for example.
As far as laws more stringent than that -- like ones we now have -- they are important to maintain stability in our country. While immigrants are an important source of "new blood" for our country, they must not be let in in unlimited numbers. We need time to assimilate the ones who are here and to have them become culturally American. That, to me, is the biggest reason to limit the numbers of immigrants.
Whether one likes it or not, the people and government of every country have the primary responsibility of protecting and promoting the interest of its existing population or citizen. This self-interest of countries is not served by being totally blind to the problems of people in other countries. At the same time a country cannot serve the interest of its people by allowing unrestricted access to people from other countries to come and live in the host country.
A country sometimes allows some people to come and live in the country for humanitarian ground. However most of the immigration is allowed by a country in the interest of the country it self. The growth and prosperity of a country depends among other things on the ability of its people to make best use of its resources. Usually, a country is not able to provides sufficient manpower of all types for balanced growth of the country, and a country has to allow and even encourage immigration to meet this kind of shortfall in specific type of manpower.
In this process of getting manpower from other countries to cover the shortfall within the country, the immigration laws serve several purposes. First, they regulate the number and type of people migrating in line with the requirement of the country. Then, they try to ensure that more qualified and capable people get preference for migration over the others. Finally, they try to reduce the cultural stress that a country may experience in assimilating within its society, in too short a time, too many people with drastically different cultures.
Thus it is in the interest of almost every country including USA to allow some amount of immigration, and at the same time regulate the immigration by suitable laws.