Then your considerations are wrong. They are a part of those legacies, whether you think so or not. Jay especially. Go pick up an issue of The Flash and see for yourself.
Yeah, I mean, it's not like Jay Garrick has been a consistant supporting character in "The Flash" for years... oh, wait.
Incorrect. The source of Alan's power, the Starheart, was assembled by the Oans (thank you, retcons). There is also a connection to an ancient member of the Corps, but I can't remember exactly what it was.
So? That's twenty-one years--only nine short of Barry's run as the Flash, and one longer than Wally's. Let's be realistic here: this has nothing to do with the beginning of the legacy. You just don't want him in the film. I don't either, but at least I'm not dishing out faulty arguments as to why.