I guess a court will have to decide or some dozen already have
best I can understand the taking prohibition (can be taken but just compensation must be paid in return) -- it does not center around public use
the operant word being "use"
how about
to promote the public interest to promote the public good
Those are phrases I see in the literature and descriptions A taking of 80% of a company and via a sale to private individuals the collection of say 80B dollars used to pay down the deficit or fund a key piece of legislation would In My Opinion be ruled as a taking for public interest or public good
My understanding of your definition is that the taking requires the GOV to then use and own it (for some prolonged period of time). I think the GOV can prompt a taking (requiring just compensation) when it takes property - ownership - for more general public interest or public good