The issue that kills Edgar is he did not start playing regularly until age 27. As a result, his "counting stats" - lifetime counts for HR, RBI, and hits - are pretty much a total miss for HOF quality.
Now, that being said, had he played for NYY or BOS, he'd already be in. His contribution to MLB transcends lifetime numbers, because his contribution was to be the quintessential DH.
But there's just no getting around that Frank Thomas, Jim Thome, Harold Baines and quite a few other guys have put up career numbers as good or better in terms of HR totals or hits totals than Edgar. Now that Thomas is in the HOF, maybe we can get Edgar in there too.
There's also always going to be a dipshit NL contingent who will never vote a "pure DH" into the HOF, because they like to think of themselves as keepers of the purity flame of "real" baseball, and this is their given right in the world. I am from the midwest originally, back in the 80s you'd see these guys write for St. Louis, Chicago, and "sporting news" style media. It's possible this has evolved out and died by now, but I doubt it completely. We were pretty smug pro NL rules in the midwest, we were certain that the DH was an abomination before the baseball gods, "Death before DH" was a bumper sticker seen around areas with big NL fan bases.
I am 100% in favor of Edgar being in. I saw him play here, he was as pure a hitter as the game has ever produced. But those career numbers will hamstring him. Eventually hopefully the Veterans' Committee will do the right thing, but I don't see the sportswriters doing it, too many of them don't know the Seattle perspective on this stuff at all, nor do they care to.