The 10th Amendment does not provide near-absolute sovereignty for the states. I'd like to hear your argument that it does.
I don't think the Framers intended for either the states or the federal government to have "near absolute sovereignty." They wanted checks and balances. If they wanted sovereignty of anyone other than the people, they wouldn't have rebelled against England in the first place.
The Constitution exists, not to give power to the federal government, but to limit its power. Article I, section 8, in particular, enumerates the twenty powers of the Congress and then gives them the authorization to enact laws to fulfil their requirements under those powers. Section 9 further limits what Congress can do within their stated powers. Section 10 then imposes some very broad limits on the states.
The 10th Amendment then says that "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."
Sounds to me like the Framers intended to limit the Federal government's power to the few items that only a centralized government could do well. Everything else (including, IMHO, the right to leave the Union) was to be left to the states and/or the people.