Actually, the last bit says that if private property is taken for public use just compensation must be given; it doesn't say anything at all about taking private property for private use. In a strict reading, that clause would not be violated if the government took my house and gave it directly to you without any compensation at all, so one would have to hope that it wasn't done with "due process of law". It doesn't say anything at all about it only being OK to take private property if the use is public.

In general, the body of interpretation and mutual understanding that we refer to as the Constitution is a pretty good effort, but I would be much happier if I actually saw a solider connection between the rights we assume we have and the actual words in the document. Still, I think what we have is much better than what we'd get if We The People had to write a new one today.