The Tenth Amendment does not contravene Article 4 Section 4, nor does it give the states “nearly all powers”—certainly not any power to turn from republican governance to socialist.
As I understand the Constitution, states are pretty much free to do whatever they want, unless it is specifically prohibited by the Constitution. States regulate issues such as marriage, abortion, automobile because they are not covered by the Constitution. States even have the power and authority to set up an official state religion (the federal government cannot of course) if they so wanted to.