It does not. The 10th Amendment reads, "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people." The power to approve any change in the status of a state, from admission to secession, is a power delegated to the United States. The fact that some of that is implied is meaningless because the Supreme Court recognized the existence of implied powers in the McCullouch v. Maryland case, and makes no distiction in validity between expressed and implied powers.
To do so would nullify the purpose for the expression in the first place. Those powers NOT given to the general government are retained to the States.
"Among the enumerated powers, we do not find that of establishing a bank or creating a corporation. But there is no phrase in the instrument which, like the Articles of Confederation, excludes incidental or implied powers and which requires that everything granted shall be expressly and minutely described. Even the 10th Amendment, which was framed for the purpose of quieting the excessive jealousies which had been excited, omits the word "expressly," and declares only that the powers "not delegated to the United States, nor prohibited to the States, are reserved to the States or to the people," thus leaving the question whether the particular power which may become the subject of contest has been delegated to the one Government, or prohibited to the other, to depend on a fair construction of the whole instrument. The men who drew and adopted this amendment had experienced the embarrassments resulting from the insertion of this word in the Articles of Confederation, and probably omitted it to avoid those embarrassments. A Constitution, to contain an accurate detail of all the subdivisions of which its great powers will admit, and of all the means by which they may be carried into execution, would partake of the prolixity of a legal code, and could scarcely be embraced by the human mind. It would probably never be understood by the public. Its nature, therefore, requires that only its great outlines should be marked, its important objects designated, and the minor ingredients which compose those objects be deduced from the nature of the objects themselves. That this idea was entertained by the framers of the American Constitution is not only to be inferred from the nature of the instrument, but from the language. Why else were some of the limitations found in the 9th section of the 1st article introduced? It is also in some degree warranted by their having omitted to use any restrictive term which might prevent its receiving a fair and just interpretation. In considering this question, then, we must never forget that it is a Constitution we are expounding." -- Chief Justice Marshall, 1819
No, the power is to admit, not control.
Controlling a State after its point of admission is against Article 4 Section 4 The United States shall guarantee to every State in this Union a Republican Form of Government,
I've already posted Rawle, who specifically says a state could leave.
§ 1819. It may not be amiss further to observe, (in the language of another commentator,) that every pretext for intermeddling with the domestic concerns of any state, under colour of protecting it against domestic violence, is taken away by that part of the provision, which renders an application from the legislature, or executive authority of the state endangered necessary to be made to the general government, before its interference can be at all proper.
Joseph Story, Commentaries on the Constitution
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Tell me NS, if an acquaintance should come to your house and you invite him in, and after a while he decides to leave, do you have the legal authority to make him stay against his will?
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Chief Justice Marshall, 1819
Marshall was speaking about whether or not a national bank was constitutional. Of course it was. The federal government was instituted with the monies from the several states, they had to have some way to deal with it.
Although, among the enumerated powers of government, we do not find the word bank, or incorporation, we find the great powers to lay and collect taxes; to borrow money; to regulate commerce; to declare and conduct a war; and to raise and support armies and navies. The sword and the purse, all the external relations, and no inconsiderable portion of the industry of the nation, are entrusted to its government. It can never be pretended that these vast powers draw after them others of inferior importance, merely because they are inferior.
Marshall also said:
We admit, as all must admit, that the powers of the government are limited, and that its limits are not to be transcended. But we think the sound construction of the constitution must allow to the national legislature that discretion, with respect to the means by which the powers it confers are to be carried into execution, which will enable that body to perform the high duties assigned to it, in the manner most beneficial to the people. Let the end be legitimate, let it be within the scope of the constitution, and all means which are appropriate, which are plainly adapted to that end, which are not prohibited, but consist with the letter and spirit of the constitution, are constitutional
He says to stay within the Constitution. The same thing I've been saying all along.