It’s not a question of why.
Rights are unapproachable. If it is my right, I can do it just because I wanna.
This question is more of an academic question, because it is unlikely to actually happen unless relations between the federal government and states get really bad.
If Kentucky threw out the Federal government, what is the process to reclaiming any federal property for the state?
Depending on if an election year, if the feds properly bought the land under either Article I, Section 8, Clause 17, or the 5th Amendment, then the feds could sell its properties in my non-expert opinion.
"Article I, Section 8, Clause 17: To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, byCession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be [emphasis added], for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings;--And"
"5th Amendment: No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation [emphasis added]."