So the ~120B is asked by a public administration for protection of general public. So it is for public use.
Nice try, but you're wrong again. The property in question, a proportional ownership in FnF, is not for public use. The problem with a taking is when the government takes property for its own use.
Also, FnF are private companies and they are the ones that benefit from the infusion of capital. The new buyers benefit because the shares that they buy are expected to appreciate in value, else they wouldn't buy them. Private gain on both sides, while the government doesn't directly benefit. So you're wrong on both fronts.
And do you really think that Calabria and Ackman would both talk about secondary offerings if they really violated the Constitution? Both of them are too smart for that.
You also aren't thinking of the flipside: if the secondary offering really is illegal, FnF will never get recapped and current common shareholders will just lose money. A new adminsitration can kneecap the entire process, and Calabria said that retained earnings alone take far too long.