Kaepernick was already pretty badly dinged up by the time he was unemployed. If I recall correctly, he had multiple surgeries in those last 1.5 years of his time with the 49'ers, and running quarterbacks who have injury question marks are a poor commodity indeed.
If Robert Griffin III can't find anything other than a backup position (with his much superior arm and decision making) these days, I strongly doubt anyone would think about signing Kaepernick except for political reasons.
I suspect that Pete Carroll simply wanted to win a few brownie points with the politically correct crowd with his words, or else he would have taken a chance on him later.
He was already not considered a good QB who could elevate your games. While he did a decent job as a game manager during Jim Harbaugh's years there, with that supporting cast around him (and that excellent defense), you could probably have stuck Ryan Leaf in as the starter, and they would have done just as well. Keep in mind, I strongly disliked Jim Harbaugh, even before he became a coach, so it's not pleasant giving Harbaugh some praise... .
When that defense was dismantled, and Kaepernick was called upon to be the one who could make the difference, he couldn't do it. The best he could do was shine during garbage time when defenses were playing deep zones to bleed off the clock, willing to sacrifice points and yards in order to kill off the remaining time.
Just as a reference, the list of available free agent QB's out there shows that there are plenty of better choices.
Link: Available free agent QB's