As someone who was one of the most frequent karma players last season I feel like I need to step in here.
If karma were able to use Focused resolve on minions/monsters she would go from her powerful healthy state into being... way to strong.
you pretty much hit the nail on the head saying she is an extremely effective 1v1 champ. But you are largely wrong about most of your other points. The truth is she has pretty excellent objective control with he empowered Q. She also has strong CC with her skill shot AoE slow, Slow zone if empowered, combined with her W root and speed boost shield she could pretty much secure kills with incredible ease as a jungler and that is a major understatement.
Truth is Karma could quite easily become a fringe power case at any moment. The fact that she is most frequently played as support keeps her shielded from that though thanks to supports typically not being able to build as much early AP. Her abilities all have a decent AP ratio and when mantra'd they are better than some of the most powerful mages in the game.
If she was able to use W on minions/monsters, even if it were only large/epic monsters, she would end up tipping the scales of OP more than you could imagine. Saying she would have poor objective control... that would be a gross inaccuracy. If she were allowed to W dragon she could take it at lvl 3 with blue buff without even the fear of dying. Why? you are forgetting about Renewal (mantra'd W). Renewal restores 20% of missing health on cast and another 20% on completion. That would be in addition to her shield which mitigates extremely well even at low ranks. Simply put... it just wouldn't even be fair.
Karma is in a perfect spot right now. Letting a champion be able to play everywhere is not healthy for the game. Thankfully, Karmas semi restricted range helps keep her from spilling over the top and I for one want to keep it that way. Any changes of this scale would put her in the cross-hairs of an enormous nerfalanche that would leave all of you who would like to see this happen crying in its wake.
(dont get me wrong, I would love if this were possible. I just know it cant and should not be done.)
for those who were familiar with the summoner play frequency of karma last season, I am ColdmanJ. At my peak I believe I reached 7th most frequent karma player in the world. The only reason I fell below the top 10 before the preseason started was that I began searching out new picks for the up incoming season in addition to Karma. I recently did a name change which is the only reason why I even bring it up.