This is an odd one. Curious as to the original source (before 1000).

Sentence core:
Building X would constitute a wasteful use of Y, (modifier).

Meaning:
Building X would be wasteful, at the very least because of one particular reason. (It's not the only reason, but it's a large enough reason that it is sufficient all by itself as a reason not to build.

C changes the meaning - it indicates that the duplicated facilities thing is the ONLY reason why it would be wasteful, but that's not the original meaning. Eliminate.

D also changes the meaning. The modifier is supposed to be a reason why building is wasteful. The use of "while" here seems to be introducing a new general piece of info, not providing that piece of info as a reason not to build.

A's modifier has multiple prepositional phrases in a row. That's often a warning sign on this test - the GMAT writers generally prefer to avoid 3+ prepositional phrases in a row.

The placement of the word "alone" also is a bit problematic. Logically, we know they're trying to say "for this reason alone" but just that word alone could also be interpreted to mean "facilities alone" - as in, facilities by themselves, with nothing else around them. Finally, the "alone" part of the meaning here is a key part of what ties the main clause to this modifier: X is wasteful, and one reason for this is Y. So it would be better to have the "alone" language between the two - if we have that as an option in one of the choices.

B has many of the same problems as A. But take a look at E. It moves the "alone" meaning (but changed to "if only because") to the beginning of the modifier. And it make the remaining meaning very clear. Why is this wasteful? At the very least, because duplication should be avoided.

Building X would constitute a wasteful use of Y, if only because Z.

So my pick would be E.