He is one of the best defensive players of all time and in an important position. Which should be enough for the HOF and still hit well enough. His WAR from 1996-2005 is only behind Bonds and A-Rod in that time frame. Seems good enough.
I see people bringing up Edmonds and Lofton. Edmonds offense is basically even with Jones and Jones trumps him easily on defensive metrics. Jones’ dWar is 24.4 and Edmonds is 6.4. Edmonds was more flash than substance.
Lofton was very good in CF(15.5 dWar) but Lofton wishes he could hit as well as Jones. He was more of slap hitter so you can’t expect him to have the power and RBI numbers. Lofton was good at getting on base and stealing bases but teams would much rather have the 400HR/1200RBI guy.
Which is why Griffey and mays get mentioned as better players, and they are better players because they bring great defense and great to generational offense. Where as Jones is All-Time defense and average to above average Offense. But defense is part of the game and if you’re that good, you should be in the hall of fame.
I think you're underrating Lofton and Edmonds here.
Lofton did not have much power, but he did hit for average very well and got on base very well, and those make up a lot of ground on Jones' superior power. Edmonds was a class above both as a hitter, combining a good batting average with good OBP and good power. Look at their batting runs above replacement for their above-replacement seasons:
Jones - 31, 28, 21, 20, 13, 12, 9, 7, 6, 1
Lofton - 34*, 19, 18, 17, 13, 10, 9, 7, 6*, 6, 5, 5, 2, 1, 1 (* strike years)
Edmonds - 52, 42, 39, 37, 36, 23, 23, 20, 17*, 14, 9, 4
Lofton of course also added a ton of extra value with his legs (+102 runs, compared to +8 for Jones and -4 for Edmonds).
The gap, of course, is significantly closed with Jones' superlative defense (+235 runs), but Lofton was no slouch (+108) and Edmonds was also quite good (+37). Eliminating poor years and focusing on peak pretty much shows the same overall results.
In the end, the three all come off pretty close to each other - 68.4 WAR for Lofton, 62.7 for Jones, and 60.4 for Edmonds. by WAA, they're also pretty close - 38.4 to 35.0. Lofton looks a little better because he was never really bad (save for his 1991 cup of coffee, Lofton had positive WAR every season of his career, and positive WAA for every year save two). Sorting by peak seasons shows basically the same results.
Basically, Jones had one area where he was maybe the most talented player in the history of the sport (defense in center field), but he did not really dominate in other areas that two of his contemporaries excelled in (getting on base, running the bases, hitting for power), which allowed them to close the gap in overall value. I'd elect all three, but I do not see any of them being clearly ahead of the other two, though if push came to shove I'd pick Lofton.
I can see an argument that the greatest ever in one area deserves more consideration, and Jones does have a very strong case as the greatest defensive center fielder ever. I'm not sure I'd be convinced of that argument, though - I'm not going to advocate for Mark Belanger for the Hall, though he would be my pick for the greatest defensive shortstop in history (Ozzie Smith is close but Belanger probably crammed about as much value in significantly fewer innings; Smith belongs because he was also a better hitter and baserunner and is clearly qualified in overall value).
Why should it not carry a lot of weight? Half of your job as a position player is defense. His defense is as good as it gets in the history of the game.
Half of your job in terms of time, but not half of your job in terms of value. The bulk of a position players' value is in their hitting (in aggregate), because the replacement value of a fielder is much higher.