"right to life, liberty, and the pursuit of happiness" is located in the DoI, not the constitution. A right to Life, liberty, and property cannot be removed without DUE PROCESS OF LAW is in the constitution, twice. I'd also like to point out the constitution is mainly a grant of FEDERAL power (and yes I understand it also addresses some state powers).
The authority to construct roads is only addressed in the constitution as it relates to the postal service (power to post roads). Taking property to build roads is also addressed. Further, the federal government has the power to regulate interstate commerce which relates more to goods that pass through states. So the remainder of power is with the states. There is nothing in the constitution that forbids a state from regulating public goods built with public funds. Your line of thought here would lead one to the belief that the state has no right to build a road to begin with. This is absurd. Citizens can give authority to the state to both build and regulate roadways so long as it doesn't prohibitively impact interstate commerce.
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