The vulnerability of supercarriers is a myth. See [1]. TL;DR: ocean is so big that it's very hard to locate and keep track of a carrier group, especially when it takes active measures to avoid location.
I have to agree with this line from the report you linked: "However, it is a reasonable assumption
that adversaries will eventually devise targeting techniques, especially in the littoral areas adjacent to their homelands"
If China wanted to, they could develop the capability to track aircraft carriers -- especially within striking distance of the mainland.
But there's a much larger implicit assumption threaded throughout the report -- the assumption that our aircraft carriers will be cruising at full speed and on high alert in prepared and competent battle groups at time of attack. The assumptions of a maximally defensive posture and extreme competence are present in virtually every argument advanced by the report.
The most significant US naval defeat -- in which damn near the entire Pacific fleet was wiped out -- suggests that a full threat assessment should relax most or all of those assumptions.
[1]: http://www.lexingtoninstitute.org/wp-content/uploads/aircraf...