That '85 Royals team had several Hall of Castro candidates: Biancalana, Onix Concepcion....and despite his slugging numbers in the mid-80s, I never really ever got Steve Balboni.
Another guy who wasn't worth the power he brought to the table was Jim Presley. In fact, I suspect we could blow this thread well past 10,000 posts if we concentrated on members of the 70s and 80s Mariners teams.
While in retrospect he wasn't THAT bad, 8 year old me couldn't for the life of me figure out why Scott Scudder was allowed on a major league mound.
Otherwise, I might go with Neifi Perez (since when did being merely poor at everything and not sucking horribly at anything mean you were a decent player?). Though the worst hitter I've ever seen was Aaron Harang. He looked like a regular Joe was pulled from the stands.
I first questioned it with regards to Denis Menke and others put forward questions about some others. The blog about the worst players ever was interesting, although I think it fell short in some cases since, it seemed to me, it was looking at one particular statistic (WARP). No question some named there (Doug Flynn and Jesus Alou are two that come to mind from that article) and yet, each had some moments where a case could be made for them having been on a major league roster.
Even a Brandon Larson, I understand how he ended up on a major league roster (and he really didn't collect a full season of games) even though his career fell far short for what had been expected of him - and his minor league numbers hinted at. History is replete with guys that didn't translate at the major league level.
Some named, for the most part, were quickly relegated to bench players with limited playing time. And absolutely, one must wonder how they ever saw the light of day as a player. I often wonder about Ed Armbrister, although it's always interesting to me to see the AAA seasons he put up before joining the Reds during the few years he was there. There are a huge number of players who played some role or another filling out some roster or another - maybe even merely being in the right place at the right time.
Perhaps the keenest observation was the comment that everyone of these players at some point in their life were among the best players from where they came from and each of them played major league baseball when so many others didn't.
It's an interesting question, but I don't think we've scratched the service of actually naming any but a small handful of players that meet the limitation in the original post. Of course, that's just my humble opinion.
Jimmy Prestley is the reason Edgar won't make the Hall