Obi-Wan's problem is that he's a young man barely out of training himself training an even younger man having problems being a Jedi (a similar mistake made with having Anakin train Ashoka Tano, IMHO-Anakin's an unorthodox Jedi training a younger orthodox Jedi who doesn't have the same problems being
a Jedi like him {although she too is somewhat reckless and prone to go off script.])
I don't think assigning newly Knighted Jedi with Padawan's of their own is a "mistake" but rather par for the course.
I know it's not canon, but the 'Path of the Jedi' book proposes a notion that I find quite appealing. That passing on their knowledge to another is the final trial of a Jedi and *that* is what qualifies a Jedi to the rank of Master. Think of a Knight as roughly analogous to a journeyman. They've completed their apprenticeship, but still must create a masterwork to present to the guild to be considered a master in their own right.
I think it really speaks to the notion that the Jedi were originally teachers, first and foremost. Monks, who gathered and shared knowledge and that the warrior thing came later and only gradually over time.
This also seems to be expressed in the way the Jedi interacted with the clones. They began to mentor them on more than just military matters. It wasn't like it was a conscious decision either, it's just how they think.
Anyway, the point of assigning Ahsoka to Anakin was twofold: first, Ahsoka was brash and impatient. Yoda hoped that when faced with this, Anakin would see that in himself and in teaching her, would also learn about himself. The second part is that eventually, the teacher must let a student go and come into their own. Yoda wanted him to learn about letting go of his attachments.
It didn't work because it all went to hell before any of that could really come to fruition. One would expect Ahsoka to have been with him for several more years and that the manner of her leaving would be passing the trials and becoming a Knight, not walking away from the Order in disgust. So yeah, it massively backfired.
Combined with Obi-wan's talents or Ahsoka to keep him centered, Anakin Skywalker was basically the unstoppable Jedi hero of the Republic. At least as far as the public was concerned.
I know this was a thing in the EU, but I'm not convinced it was ever really the case. I get the impression that Palpatine's propaganda at the time would have been careful *not* to publicise the exploits of any particular Jedi as individuals.
This would both please the council who certainly aren't interesting in their Knights and Masters becoming galactic celebrities and serve Sidious's ends in (for lack of a better term) dehumanising the Jedi and casting them as a monolithic cult of war crazed zealots in the public imagination.
I wouldn't be surprised if the involvement of the Jedi went increasingly omitted from news reports as the war went on, crediting only "Republic forces" with victories. The failures on the other hand, would be a different matter. Indeed, I imagine that after a while, the only time the word "Jedi" would appear in the news is when Palpatine would publicly "defend" them against accusations of excessive force, inept leadership or in needlessly perpetuating the conflict.
I'm sure they'd also not miss an opportunity to refer to the leader of the Seperatists as "
former Jedi, Count Dooku", just to reinforce the negative connotation in people's minds and fuel the suspicion the Jedi are behind the whole thing.