I think Doriath was probably next on Morgoth's hit list by the time it fell, if for no other reason than he'd run out of other targets.
As for why he didn't do it before, he didn't really have an opportunity. There were several kingdoms in between him and Doriath.
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...finding a path that cannot be found, walking a road that cannot be seen, climbing a ladder that was never placed, or reading a paragraph that has no...
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