What
Jarmo had 2 top 10 picks. The Blackhawks had their top 2 forwards in the top 3, found a Norris trophy defenseman in the second round and is a destination for free agents. LA is a destination that their 2C essentially forced himself to be traded to.
The draft capital of a true rebuilding team was a 1st overall who blew out his knee in a freak accident and a 4th overall defender who might be having a hall of fame career. The rest of the team was built from the middle/lower portions of the first round of the draft. These areas are not gimmes. Our rebuild was shorter and we didn't have the benefit for being a premier market that the teams you're comparing us to do. We were at a disadvantage from the outset.
Jamie Benn won the rocket with 85 points in that era. Kopitar was LA's only 70 point player. You're going through as many hoops as you can to avoid giving credit where it is do. Jarmo did a good job with the rebuild. He was a poor GM in Columbus, but that doesn't effect his work with the Blues.
Let's put some numbers to this. In terms of career totals, of players drafted between '03 and '10, the Blues were 16th in the league in games played from players 31-100. Excluding Soderberg -- who didn't play until his D+8 season for a different team -- we drop to 23rd. That puts us at 20th in the league for players drafted during that time in terms of total career points scored. Backes accounts for 94% of that total. So in the 7ish years that Jarmo was at the helm of our scouting department, he produced exactly one point-producing player of any consequence -- in what is widely recognized as the deepest draft in NHL history, and one in which he absolutely whiffed the first round pick for -- from picks 31-100, which he had 24 of.
Granted, he also picked Bish and Allen. Bish got us a 2nd round pick which hardly made it past the ECHL (Vannelli), and Allen was benched midway through the '19 season for an unproven, career AHL backup who hadn't appeared in an NHL game for almost 4 seasons. Allen played one game in those playoffs. Jarmo didn't have anything to do with trading Bish (presumably), but he also didn't "break out" until almost his D+9 season. In the meantime, we wasted a lot of the draft capital Jarmo had accumulated on trading for Halak and Miller, and FA dollars on the withering husks of Conklin, Mason, Osgood, etc. A lot of that is because he swung and Linus'd on a 5'10" Czech goalie at 17th overall in '04. In that era, we spent a ton of money covering up the lack of depth that Jarmo left us both in net and beyond.
Now, over that same period of time, LA was 4th in games played from players drafted in that range, and Chicago was 20th. In points, LA was 7th and CHI was 23rd. Both of them had the advantage -- as you pointed out -- of being destination spots, or having the advantage of several closely-grouped generational draft choices. We didn't have either of those luxuries, and the one 1OA pick we did have flopped. Turns out the best and generational picks that year went 2-5.
I'm absolutely not writing off the impact of Petro, or Vladi, or Oshie, Perron, Bergie, or any of those guys. I loved those teams, they were "my generation" of Blues players. But the reality is that we spent years trying to climb out of the hole of mediocrity that Jarmo built us. It isn't that Jarmo was bad at drafting at the beginning or -- oddly enough -- the end of the draft, it's that he wasn't good enough to overcome the inherent disadvantages that playing in a mid-market city come with. He wasted a ton of draft capital in rounds 2-4 on obviously-flawed players, even adjusting for the era. Swinging for the fences is all fine and well, but a 1/24 (or even 3/24) batting average is just bad scouting. I think the fact that he and Davidson both similarly floundered in mediocrity in Columbus kind of prove that point.