With all due respect, that is incorrect. The "public use" requirement applies to all uses of eminent domain, federal, state or local. Even in Kelo (a municipal use of eminent domain), the issue was whether the transfer of property to a private developer could be a public use. The Supreme Court (wrongly) held that such a transfer could qualify as a "public use," and therefore could be permissible; had it not been a "public use," it would have been prohibited. So, no, states are not exempt from the "public use" requirement at all.
The 5th amendment originally only applied to the Federal Government, and neither imposed any legislation on eminent domain nor restricted the State's right to do whatever it pleased on the matter. The 14th amendment, in its turn, was never designed to take away any of the State's rights. So the question is, can the Federal Government stop the State from having broader or less broad eminent domain laws, provided that due compensation and due process is always kept? The answer is no.
So I took the money and they took the land and built the pumping station. So it goes. I guess I could have chained myself to a tree and become a cause celebre but I'm a busy guy and needed to get on with life.
The ultimate use of eminent domain however was when the Europeans settled North American and displaced the native Indians. So if one is opposed to eminent domain, in order to be consistent, they would have to yield up their property to the nearest Indian tribe - or at least start paying them rent.
The neighborhood my mother grew up in during the 1940s was seized, leveled and graded, and now its part of Interstate 93 just before it enters Boston. The property owners were paid above market value and they were able to rebuild elsewhere. And life went on.
Now I understand Trump was trying to build a limousine parking lot or something like that. He offered the owners a decent amount of money (million dollars for some run down shack?) and they refused. So he availed himself of the court system to try and get his way. Maybe he did, maybe he didn't. Either way, Trump didn't "seize" anybody's property. Either the courts decided it was a proper case of "public use" or they didn't.
Generally such property is for commercial purposes which equal economic development that a city/state is promoting...and which btw brings jobs.