"Why do you think that a policy that had been used for 30 plus years to admit states to the Union was repealed and replaced?"

It was replaced because Stephen Douglas and some other northern Democrats, who were interested in western railroad development, could not get Southern support for the organization of Kansas and Nebraska territories unless it was replaced. With the Missouri Compromise in place, Kansas and Nebraska would have automatically come in as free states---something quite distasteful for Southerners who wanted to keep the balance of power between free and slaves states in relative check. Douglas tried unsuccessfully to work around the Missouri Compromise, but ultimately adopted the doctrine of popular sovereignty as a neutral way of indirectly repealing the 34 year old compromise.

Of course, the Kansas-Nebraska Act did not really please anyone and probably did more to lead to the Civil War than any other single piece of legislation.

For more info, see:

Robert R. Russel, "The Issues in the Congressional Struggle over the Kansas-Nebraska Bill, 1854," _The Journal of Southern History_ Vol. 29, No. 2 (May, 1963), pp. 187-210

Frank Heywood Hodder, "The Railroad Background of the Kansas-Nebraska Act," _The Mississippi Valley Historical Review_, Vol. 12, No. 1 (Jun., 1925), pp. 3-22

Roy F. Nichols, "The Kansas-Nebraska Act: A Century of Historiography," _The Mississippi Valley Historical Review_, Vol. 43, No. 2 (Sep., 1956), pp. 187-212

Robert W. Johannsen, "Stephen A. Douglas and the South," _The Journal of Southern History_ Vol. 33, No. 1 (Feb., 1967), pp. 26-50

Or for more quick info, see:

http://lincoln.lib.niu.edu/biography6text.html

http://www.civilwarhome.com/kansasnebraska.htm

http://dig.lib.niu.edu/message/ps-kansasnebraska.html

Do you have a different explanation for the demise of the Missouri Compromise?