The Vatican gives no evidence, of course, hoping that by fiat its declaration reflects reality.
It may or may not be true that married priests would relieve the shortage of priests, but the Vatican will never know, since it refuses to discuss the issue, or even commission a study of it. "A commitment to the service of the Gospel of hope also demands that the Church make every effort to propose celibacy in its full biblical, theological and spiritual richness."
The only thing Catholics see in a celibate priesthood is a predominance of homosexuals. One thing's for sure: a married priesthood may or may not bring more men into the priesthood, but it will bring heterosexual men into the priesthood, which might be a good place to begin discussing celibacy in its full biblical and spiritual richness for those who choose to accept it.
Catholics also see married Protestants being accepted into the priesthood, and many are scratching their heads trying to understand why married life-long Catholic men aren't deserving of the priesthood, too.
I've noticed the Vatican seems to issue one of these "celibacy forever" documents on a yearly basis, almost as if it is trying to convince itself that, yep, we're right on this one.
On a second reading of the article, I'm wondering if the Vatican's statements are nothing but the usual boilerplate on celibacy. The timing of this document and its major theme seems to be a slap at the EU for not highlighting the role of Christianity in its constitution.