I agree with you. There has not been any evidence of it. There still teaching it though in astronomy classes.
Yes, alas, the bits of solar system debris which smack into the Earth once in a while seem to be drawn from the NEOs. There is no real pattern to it, at all, no cycle. Eugene Shoemaker thought that the apparent cycle was due to the solar system's circuit around the galactic axis, that somewhere there was a bunch of crud we'd pass through. The question I'd have is, why doesn't that bunch of crud also make the circuit? I don't think E.S. thought that through very well.