I have been playing Pokemon Platinum recently to revisit the generation 4 world with a few game limiting self imposed rules, and long story short, I had to challenge the second gym (grass type) twice. The first time was with weak to neutral type match ups, where I had an enjoyable battle, just falling short of the victory. The second time I took in 1 super effective bug type with a "same type attack bonus" (STAB) move, which deals 2x and 1.5x damage respectively, and swept through using only that Pokemon.
The mechanic here of how powerful super effective STAB moves are needs to be toned down. I like the idea of each of these mechanics on their own (STAB move but not super effective...) along with the benefits they grant, but together it may need to be modified to stop the pattern of 1 or 2 hit knock outs being the most viable and enjoyable method of battling. I like to use my entire arsenal of supporting moves (status effects, stat manipulating, regenerating moves) but these are vastly over shadowed by the effectiveness of turning into a 1 punch man.
I think a simple lowering of the numbers is what is needed to eliminate the power creeping of damage dealing moves. This in affect should create more interesting and dynamic battles, which in their own way can be a personal story rather than a game mechanics to move the plot along. The battles can then be stories in the same way that "an underdog sports team wins the championship", or how a celebrity is villainized by the media is a story (2 extra-contextual examples in the normal world, which I am uncertain about their validity, for the non-nerds out there). Also this would allow for specific Pokemon to still be usable in all or most situation while still being at a disadvantage. Currently I feel it is presented that a Pokemon is either not usable, or the only usable option in a battle.
As a note: this does not apply to the competitive battling scene or any Pokemon related interactions not designed for a 6 year old or a 6 year old at heart.