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The states freely withdrew their representation when they began their rebellion. They willingly participated in the rebellion. They accepted the results of their actions, and that included keeping those who led the rebellion from returning to Congress as if nothing had happened.

Perhaps you'd be interested in the view of the Detroit Free Press about the conditions the Union placed on Southern states (The Memphis Daily Appeal, [Atlanta, Georgia], February 26, 1864):

How the States are Brought Back Into the Union
Not all the Northern papers endorse Lincoln’s farce of "dragooning" the seceded States "back into the Union." The Detroit Free Press (the organ of General Cass) says of the game being played in Arkansas:
The President says to the people of Arkansas: I will allow you to return to the Union, but not under your own Constitution and the Constitution of the United States. You must first join the abolition party, and next you must make – or I will make for you – an abolition Constitution and abolition laws. If you don’t do this, I’ll send an army there to thrash you till you do it. I’ll send Northern politicians to rule you – some consistent bantam like T. W. Lockwood, or some virtuous chieftain like Colonel Dorus Fox [I think he may have been charged with buying commissions]. I’ll make you a Constitution and enforce it upon you by bayonets, and the First Michigan Ethiopian. It is my will, and you must submit. You must accept this "unconditional Unionism." The interests of God and humanity require it, and the people of Massachusetts wish it.