Mixed Metaphor
I see number two as those who made a confession, but never had a possession. Those who took up membership, but never had the real thing called salvation. They thought they were saved, but never produced any fruit. And when the times came that Satan assaulted them, they, having no root(Jesus), withered away.
Both 2 and 3 professed faith in Christ, but profession does not save. Only when God credits our faith, as flawed as it must be, as righteousness, are we set apart in Christ and undergo the circumcision of Christ.
Lots of people have a fuzzy view of exactly what saves us, when scripture says it is God who puts us "in Christ" our ark.
Yes, when we examine ourselves at communion, to see if we are "of the faith" what do we look for? A public profession of faith? Nope. A changed life diligently striving to follow Christ and become more like Christ? You bet!
I though it was an interesting claim that soil number 2 having no root in himself referred to Jesus who is the root of Jesse and root of David. But I think that is mixing metaphors. The root in view in the parable has to do with deep conviction, i.e. heart felt rather than head knowledge. They believe but not from the heart, thus no root. Rocky soil speaks of soil that is thin, over hard rock. They lack cultivation to break up the hard ground so the word can sink deep. They want the fire insurance but do not want to become partakers in the suffering of Christ.
Grace came to him and he accepted. The healthy do not need a doctor. Hard to deny an offer of help like that.