This unrequited fantasy “love story,” a love story unknown to the victim/s, has always been IMO the primary and likely motivation.
We see this need for reciprocal love and validation even in celebrity stalking situations. The “fan” believes he or she is bonded to the celebrity, that the celebrity is speaking directly to the “fan,” and if they would only meet, they would have an intensely close, mutually fulfilling relationship.
It doesn’t even have to be a sexual or romantic connection. Just a feeling of overwhelming desire on the part of one to be close to the other. Then they make that attempt, their all-or-nothing consummation of their dream to be together, and they get ignored or shut down.
Then, as you’ve both stated, the burning for ultimate control can lead to the destruction of the idol, or idealized romantic partner.
For example, John Lennon and Mark David Chapman, or the fictional “Stan” about whom Eminem wrote.
I’m open to a different paradigm, though, but I still lean greatly towards this early theory.
JMO