It's ludicrous to claim that the constitutional form of government violates the Constitution. Since apportionment of federal senators by state doesn't violate the Constitution, apportionment of state senators by county doesn't either.
States are sovereign, counties are lines on a map. The county that I live in is an artifact of a feudal Dutch patroonship and was 3x larger a 150 years ago. A county about an hour from me is the legacy of a land-grant to a revolutionary war hero and is mostly berfit of people. Why should a mountain be better represented than my family?
Apportionment of US Senators doesn't violate the constitution because it is explicitly referenced in the constitution. The Senate has always been a reactionary force in US politics, placed there to ensure the political power of the south -- since their population of "human chattel" would have limited their political influence. The openly corrupt nature of it's early makeup (ie. no direct election of Senators) was partially addresses via constitutional amendment. The legacy of the Senate isn't pretty -- it is directly responsible for the system of vigilante lynching that terrorized the south, for example.
What's ludicrous is replicating that legacy of regressive policy and difficult to hold accountable representatives in other layers of government.
They were, among other things, aping the British system, where a reactionary upper house was an old feature.
From 1882-1968, over 200 bills were introduced in Congress to make lynching a Federal crime. 7 US presidents called upon congress to address the issue in legislation as late as 1952. None made it through the Senate, I don't recall exactly, but I think that only one made it out of committee. The "solid south" Senators kept these measures bottled up.
Only the extraordinary abilities of LBJ was able to break the ossification in the Senate the blocked civil rights.
From President Truman's Commission on Civil Rights, about two of the "less brutal" lynchings in 1946:
"On July 20, 1946, a white farmer, Loy Harrison, posted bond for the release of Roger Malcolm from the jail at Monroe, Georgia. Malcolm, a young Negro, had been involved in a fight with his white employer during the course of which the latter had been stabbed. It is reported that there was talk of lynching Malcolm at the time of the incident and while he was in jail. Upon Malcolm's release, Harrison started to drive Malcolm, Malcolm's wife, and a Negro overseas veteran, George Dorsey, and his wife, out of Monroe. At a bridge along the way a large group of unmasked white men, armed with. pistols and shotguns, was waiting. They stopped Harrison's car and removed Malcolm and Dorsey. As they were leading the two men away, Harrison later stated, one of the women called out the name of a member of the mob. Thereupon the lynchers returned and removed the two women from the car. Three volleys of shots were fired as if by a squad of professional executioners. The coroner's report said that at least 66 bullets were found in the scarcely recognizable bodies. Harrison consistently denied that he could identify any of the unmasked murderers. State and federal grand juries reviewed the evidence in the case, but no person has yet been indicted for the crime.
Later that summer, in Minden, Louisiana, a young Negro named John Jones was arrested on suspicion of housebreaking. Another Negro youth, Albert Harris, was arrested at about the same time, and beaten in an effort to implicate Jones. He was then released, only to be rearrested after a few days. On August 6th, early in the evening, and before there had been any trial of the charges against them, Jones and Harris were released by a deputy sheriff. Waiting in the jail yard was a group of white men. There was evidence that, with the aid of the deputy sheriff, the young men were put into a car. They were then driven into the country. Jones was beaten to death. Harris, left for dead, revived and escaped. Five persons, including two deputy sheriffs, were indicted and brought to trial in a federal court for this crime. All were acquitted.
These are two of the less brutal lynchings of the past years. The victims in these cases were not mutilated or burned."
It's not ludicrous to claim that the Constitutional form of the federal government would, if replicated in the states, violate a constitutional restriction that applies only to the states, which the Equal Protection Clause does.