I think it had the soul a lot more than it will ever be given credit for.ST 2009 did pay homage to TOS in the ways that you described. But those similarities were essentially superficial. The movie moved at warp speed with all the explosions, shoot outs, etc. It didn't have the same feel as TOS.
I am going to borrow a line that Kirk spoke in "The Return of the Archons":
"The original Landru programmed it with all his knowledge but he couldn't give it his wisdom, his compassion, his understanding, his soul, Mister Spock."
JJ Abrams may have directed the ST09 movie with the knowledge of everything about TOS that came before, and he may have genuinely tried to pay homage to TOS; however his movie lacked the soul that made TOS TOS. Maybe it just wasn't possible.
Having said that, I still found the movie fun to watch but not nostalgic.
Largely because, what made Star Trek special was in the characters, and their connection with each other. ST 09 took those connections and changed them, allowed the characters to explore new relationships. In essence, Star Trek grew a little bit, changed up the dynamic, and went on to explore what made those relationships special through those changes.
I listen to a couple of podcasts and there were some points made that felt applicable. The first one was on the idea of Star Trek as a friend that we don't want to change. In real life we would want our friends to grow and change and become something different, even if we don't agree with the choices made, they are still a friend.
The second podcast was in terms of Star Wars, but I think the attitude still applies. The original series and original Star Wars film could not be perfectly replicated. Why? Because mistakes would be made that they would learn from as they go. Like a band that gets back together, they will make different mistakes because they've already learned.
So, in one way-you're right. The spirit couldn't be captured. In another way, it did because it focused on the characters, the relationship against the backdrop of action/adventure series.
Sure, it's subjective. Which, and call me crazy, but that's why I will appreciate the Paramount and CBS rather than random fans.That too is in the eye of the beholder.