The Takings Clause reads, "…nor shall private property be taken for public use, without just compensation." This has always been interpreted by courts to forbid taking for anything other than a "public use," compensated or otherwise. One can summarize the reasons for this interpretation as follows:
(1) It’s the common-sense way to interpret the clause in light of the rest of the Constitution (e.g. in light of the rest of the 5th Amendment, by the doctrine of enumerated powers, by the 9th and 10th Amendments, by the interpretation rule of smaller to greater, etc.)
(2) Precedent: the Supreme Court has always interpreted it that way. The big dispute is not over this, but over what "public use" means. Alas, the preposterously broad Kelo definition of "public use" makes the complement category "private use" almost a nullity.
I’d add that forbidding of takings for private use reflects what English common law and state practice (interpreting similar provisions in state constitutions) was at the time of ratification. The framers simply took it for granted, thus the poor wording.
(The framers realized such dangers of misinterpretation generally, however, which is why we have the 9th and 10th Amendments: to prevent construing of poorly worded clauses against individual rights).
There are also good policy reasons to forbid takings for private use, such as the public choice waste that arises when B lobbies officials to take A’s land for B’s use.
Which brings us to why Kelo wasn't even close to an accurate opinion about the law. The "public use" in the 5th Amendment probably referred to Hale’s "public interest" doctrine, which when the 5th Amendment was ratified meant only functions involving either coercion or monopoly – for example a police station or courthouse, or the equivalent of taking a toll on the only bridge across a river. A franchise was, to quote a modern movie, a business that could legally make "an offer you can't refuse." It was as a result closely regulated under common law. The most common requirements were that it had to be open to the general public, that the service be well maintained, and that it was restricted to charging only "reasonable" tolls.
It is thus unconstitutional to take private property for the use of any competitive enterprise (even if it’s run by government). There are almost surely also Due Process Clause restrictions to taking property, even for a coercive function or a monopoly, when that involves "taking from A to give to B" (to paraphrase Sir Edward Coke in the 17th century and Justice Samuel Chase in Calder v. Bull), and to take property such as a house or communications device used to exercise a fundamental right, as I describe here. But U.S. courts don’t recognize those rights either.
Around the time of the ratification of the U.S constitution, state constitutions that specified language like the U.S. constitution, and generally under common law, forbad takings (compensated or not) for non-"public use." There are two somewhat different issues here, since there were two different interpretations of what was forbidden as not "public use." The first forbad a taking from A to give to B rather than to a government. The second (and I believe correct) approach forbad taking for the use of a competitive enterprise, i.e. an enterprise that did not under the old common law require a special patent-like property right called a "franchise." A franchise was required, per Hale, for a natural monopoly which charged a "toll." A franchise could also be a privately owned court or police force (these were common in England, and there were some private courts in some U.S. colonies, but these had largely disappeared in the U.S. by the time of the ratification). A franchise was required by common law to be open to the public and charge a "reasonable" toll, unlike a competitive enterprise which could charge the market rate.
On the first interpretation(whether private property could be taken from A and given to B), the following claims in early Supreme Court majority opinions are a bit exagerated, but generally correct:
"...a law that takes property from A. and gives it to B: It is against call reason and justice, for a people to entrust a Legislature with SUCH powers; and, therefore, it cannot be presumed that they have done it. The genius, the nature, and the spirit, of our State Governments, amount to a prohibition of such acts of legislation." Calder v. Bull, 3 U.S. 386, 388 (1798)
"We know of no case, in which a legislative act to transfer the property of A. to B. without his consent, has ever been held a constitutional exercise of legislative power in any state in the union. On the contrary, it has been constantly resisted as inconsistent with just principles, by every judicial tribunal in which it has been attempted to be enforced.... The counsel for the plaintiffs have themselves admitted that they cannot contend for any such doctrine." Wilkinson v. Leland, 27 U.S. 627, 658 (1829)On the second interpretation(whether private property could be taken for a competitive enterprise instead of a franchise) the evidence is more concrete, but misunderstood, since hardly anybody understands franchise law these days. Justice Thomas' dissent in Kelo [with my comments in brackets] gives a good overview of the case law at the time:
States employed the eminent domain power to provide quintessentially public goods, such as public roads, toll roads, ferries, canals, railroads, and public parks [all of these were, if privately held, franchises under common law -- NS]. Though use of the eminent domain power was sparse at the time of the founding, many States did have so-called Mill Acts, which authorized the owners of grist mills operated by water power to flood upstream lands with the payment of compensation to the upstream landowner. Those early grist mills “were regulated by law and compelled to serve the public for a stipulated toll and in regular order,” and therefore were actually used by the public.They were common carriers— quasi-public entities. [These were toll-taking franchises -- NS] These were “public uses” in the fullest sense of the word, because the public could legally use and benefit from them equally. See Public Use Limitations 903 (common-carrier status traditionally afforded to “private beneficiaries of a state franchise or another form of state monopoly, or to companies that operated inconditions of natural monopoly”).Thomas cites many state cases where full public access was required, or else the taking prohibited. This however is an incomplete distinction: public access was merely required of a franchise by the common law, but there were other common requirements, such as the "reasonable toll" requirement, and these requirements didn't define a franchise. A franchise was defined per Hale as a business that its "customers" could not avoid using: either a coercive process, as tax farming or operating a private court, or a natural monopoly, i.e. an unavoidable service that charged a toll.
To be sure, some early state legislatures tested the limits of their state-law eminent domain power. Some States enacted statutes allowing the taking of property for the purpose of building private roads [franchises were privately owned, so this is no exception to the rule -- NS]. These statutes were mixed; some required the private landowner to keep the road open to the public, and others did not. Later in the 19th century, moreover, the Mill Acts were employed to grant rights to private manufacturing plants, in additionto grist mills that had common-carrier duties. [citations omitted]