I assume it has to be grounded somehow in the politics of Revolutionary America, but I don't understand the connection that would cause so many to think it is not only correct but plainly obvious that states should possess sovereign immunity over citizens, or why holding otherwise is some great affront to the dignity of a frankly pretty abstract institution. But you look at the speed at which the 11th Amendment was created and ratified and the near total unanimity behind it and it's obvious to me that people took great offense at Chisholm v. Georgia. What's the deal?
The idea behind sovereign immunity is that since the state itself has sovereignty, the state can decide when laws and rule apply to it. The essence of sovereignty is a entity poses sing sovereignty is not bound to rule created by anyone, including rules that it itself created. The real issue to understand why Chisolm v. Georgia is a big deal is that by abrogating the doctrine of sovereign immunity, the Supreme Court was seen as overstepping it's boundaries and taking power away from the state that was rightfully and constitutionally within the power of the states, and giving those powers to the federal government. Some lawmakers and state governments felt that the ruling on Chisolm v. Georgia violated the Tenth Amendment, in spirit if not in letter. Thus, they worked speedily to create and ratify the Eleventh Amendment, so that such a ruling would henceforth be impossible.
The entire topic should be seen as part of a larger political struggle over the boundaries between the powers of the states and the powers of the federal government, that continued, in various forms, right up until the outbreak of the American Civil War.