I can find 5 players since WWII who are in the HOF who have less than 2,000 hits. Three started their career late because of the color barrier (Robinson, Doby and Campenella), one is in only because he was a Yankee (Rizzutto), and the other is Ralph Kiner who was the Sandy Koufax of batters. I fdon't think that helps Edmonds.
The closest player I could find to Edmonds in the HOF is Puckett.
They have similar GG and Career OPS+.
Puckett seems more consistent, did better in MVP voting, stole more bases, had a higher BA, was probably the best player on his team for 10 years and arguably the best player in the AL from like 1986-1992.
Edmonds hit for more power (although adjusted for era, I don't if it is significant), walked more, was probably better defensively, and probably not considered the best player on his team but one or two years.
I think the biggest difference (other than Pucket had to retire at 35 and probably would have compiled a few more good years of stats) is that Pucket stood out. Edmonds was the other OF for the Angels.
I don't think Edmonds is HOF worthy. I do think Puckett is. Although, this conversation has made me think more about it.