Back to the subject though: the doom wasnt just from the seeds of Morgoth. "Doom" or "fate" (if one buys into that idea) occurs or is manifested by people. The country or land that those people inhabit (to me) is secondary.
There were some major players on the stage of Doriath for many years. Melian, being a Maia who choose to inhabit that land, would (I think) have a tremendous amount of effect on the fate of any around her - more so than "seeds of Morgoth". It was her that prevented Morgoth from sullying that land, EVER. Something no Noldorian prince could say about their territory....
But, by choosing to live in ME, Melian's doom was woven with Elu Thingol, Beren, Blue Mountain Dwarves et al, including Morgoth as well. Taken all together, yea there was some mighty doom in that place. One can see this in the Ruin of Doriath: so sudden and cataclysmic. I think it was the device by which JRRT could best describe something about how no matter how well you try to protect Paradise, there is always someone (including his doom), who is gonna mess it up
