In this movie he just wanders around, kills random people at his own leisure and pleasure, doesn't seek her out at all...instead of the stupid twist with the doctor it would have been a really interesting turn to see that Laurie spent her entire life prepping for Michael's return and then it just turns out that there was no connection, no special purpose or desire, she was simply picked at random back in 78 and Michael might not even remember her. Done in a way that would not have taken a climactic ending away, just would have put it in a different light could have been really neat methinks..
As much as I like the sequels (up until the sixth one), this is what irked me the most; the ham-fisted, familial connection that was completely unnecessary. If there's any connection at all, it's that there may be a vague recognition, a tick that sets off Michael, where he kills/targets babysitters through to some loose connection with his sister originally babysitting him. But even by the film's own admission, no one knows what makes Michael single out a person and picks them as his prey. He just does. Your idea here is very much in line with what I think.
However, for sequels of him just following different people, the problem would be just that. It'd just be the same film as the first but with a girl with a different hair style. I think the only way it would work is if it all came to a head some kinda way but, again, the problem is Michael himself. He's a force of nature in the shape of a man. He can't be contained, caught, or killed. He just keeps going on and, unless the series ends, I think we're in for some more hum-drum sequels.
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...Case to point: incidents not generating consequence. The bus crash resulted in at least four murders and a missing psycho killer on the loose, but the cops aren’t bothered and it doesn’t get a mention on the news. Later there is the quadruple killing at the garage, by the same killer and the cops attitude is to ignore it again. No major manhunt, other than an old cop crusising alone around the streets, no news alert, everyone out enjoying Halloween on the street. Real world would have seen a major manhunt with everybody alerted. .
I think this would've made the movie a lot more exciting and suspenseful had everyone been on the lookout for him and shut up in their homes. Cops combing the streets with Laurie on a vigilante crusade to track him down, but Michael still eludes capture and still stalks and preys on people throughout Haddonfield.