Here's my basic attempt at a "Jermaine O'Neal is underrated offensively" argument which is on my mind. Let's play it out between him and Blake because they are similar guys.
In the seasons selected, here are some stats:
Less than 5 feet: JO 232-424 (55%), Blake 491-708 (69%)
5-9 feet: JO 127-338 (38%), Blake 40-142 (28%)
10-14 feet: JO 124-315 (39%), Blake 31-73 (43%)
15-19 feet: JO 114-281 (41%), Blake 95-226 (36%)
20-24 feet: JO 11-13 (33%), Blake 58-151 (38%)
Of those shots, here's the makeup:
Jump Shots: JO 394-1029 (38%), Blake 219-648 (34%)
Alley Oops, Layups, Dunks: JO 184-319 (58%), Blake 451-597 (76%). Notably Blake had 50 more alley oops where they both finished 80%-85%. Jermaine's FG% delta comes from layups
The rest is miscellaneous other stuff.
So from looking at that, I say that of course Blake is a better finisher. I also say that Jermaine O'Neal is actually...a better shooter! He's better or at least at par from 10-24 feet, and he's meaningfully better from 5-9 feet. Blake got way more "gimme" attempts at the rim, shooting 300+ times more there.
That gives me two conclusions. One is that Jermaine has terrible shot selection, and two is that perhaps Jermaine was on a team where he felt like he had to do that. So let's look there.
Blake's team had Chris Paul at point guard (10+ assists) and a couple capable team passing guards.
Jermaine's team had...eh, I'm just going to say it because he's not getting drafted -- Jamaal Tinsley and his 5.8 assists per game and 40% shooting at point guard. Good luck with that! At shooting guard, he had Reggie in his twilight who was never really a passer and certainly not at that age was he creating for others. Ron Artest is also a black hole on offense despite his insane abilities elsewhere. The other swing player there who could feasibly be drafted was a ball hog when he did get it. It might have been the worse ball movement team of all time!
So my point is that Jermaine may have had some bad shot selection, but his actual offensive talent level is not that far off of these other guys. Had he played with Chris Paul, he would have gotten way more rim opportunities and had to force fewer jump shots. He was asked to just take the ball and figure it out. Which he still did, but is way harder when you're double teamed every time. And they still almost made the NBA Finals.
I'm not trying to overhype here -- I think he's clearly a step below Rasheed, LMA, even another to-be-drafted guy maybe although that guy had an elite point guard. Maybe Griffin -- I'm not trying to diss Blake here either because he's quite good as well. I'm just trying to suggest that if Jermaine has guys like Penny, Marques, Westphal, and Gasol on the court with him to actually play offense, then he's not going to be such a dingus with the basketball. He's going to rim-run and use his athleticism like Kemp and Blake did. He's going to park down low. He's going to get 1x1 looks rather than double teams. That change of situation elevates Jermaine to be an offensive threat maybe not at their level but not far off it.
EDIT: It's interesting. Maybe I would take 02-03. That's a good example. He had more team oriented players on the roster (a couple I can't mention). Suddenly instead of 319 of those three types of shots, he had 123 dunks, 199 layups, and 11 alley ups attempted -- and made 69% of them. Because of that, potentially, he shot fewer jumpers (877) and made marginally more of them. So when he had a real team around him to facilitate, he had a much better mix of shot selection and a much higher rate of finishing because they were better looks. Put him in those situations and you get good results.