My guess is:
1. It's good science
2. It's glamorous and in vogue
3. Success would allow someone to decode old messages encrypted
with RSA
It's doubtful that really important secrets are still being encrypted
with RSA
Aside from factoring large numbers (which IMHO has only a very very
slight chance of succeeding) all other applications seem to be the
solution to problems that are of little consequence.
On the other hand, success would be an amazing experimental
verification of an aspect of physics that I believe has not ever been
demonstrated. In that sense research into quantum computation could
yield results as important to physics as what might come out of the
next super collider.
Finally, as 't Hooft has pointed out to me, success at factoring large
numbers without quantum computation ought to have a dramatic effect on
theoretical physics. It could help us to clarify the role of QM as a
method of calculating the probability of events as opposed to the idea
that QM is a model of reality.
Ed F