The second clause does not logically follow the first.
If there is no life elsewhere in the Universe, then it’s just a big waste of real estate.
True. That is because the phrase is really a shorthand version of the Drake “Equation” which, in turn, is itself just a very high level approximation of an equation human beings don’t even know all the terms for at present.
Properly, it should be:
The Universe is so vast ... there MUST be life elsewhere.”
The “...” representing, of course, all the various circumstances necessary for life (however you care to define it) to develop.
This, in itself, is a far less stringent condition for success than requiring the development of a spacefaring civilization in our galaxy and its explorers reaching the Earth during a time when mankind exists and is sufficiently advanced in its own right to properly evaluate their arrival. That achievement, to start out with, requires the development of life (and its elaboration) in at least TWO places vice one.