Theres nothing wrong with powergaming. I dont restrict my players character creation in the slightest. Never have. I run a sandbox game, i create situations, its up to the players to decide how to deal with those situations and if that involves diplomancy or a combat monster chopping everything to bits then fine. Actions have consequences and the campaign is the story of the journey the players are on as they go from adventure to adventure.
Nothing about powergaming detracts from that in the slightest.
It depends what you are going for. Most stories are designed to invoke emotion of some sort. As a DM, you are still a story teller. You create the situations your players encounter. Your decision to make the shopkeeper meek and shy vs overbearing and domineering invokes a very different story, very different reactions, and very different emotions.
Just like whether the players are powergamed or not can affect their reactions to situations just as much. Take the following situation:
The villagers come up to the PCs and beg them to free them from the tyrant wizard who lives in the tower on the hill.
Non powergamed characters may realize that they don't have the ability to defeat the wizard in combat so they start a rebellion and recruit an army to try to defeat the wizard. This process might take days or years to accomplish. They come up with a plan to lure the wizard out of the tower and face their army.
Slightly powergamed characters may realize that they don't need an army to defeat the wizard, they can do it themselves. So they go to the tower and fight their way through the traps and puzzles the wizard has set up over a couple of weeks of play before finally defeating the wizard in a difficult combat where they nearly die.
More powergamed character might just teleport directly to the wizard and skip his traps and puzzles before killing the wizard in the first round of combat before he gets an action.
Even more powergamed characters might simply disintegrate the entire tower and the wizard inside of it without getting close.
Each of those stories might be more or less satisfying for the players and the DM involved. And you want the DM to enjoy the game that is being played. A DM who becomes dissatisfied with the story his game is generating might simply decide to stop running the game because it doesn't bring him the joy he wanted.
Not every GM can dispassionately sit back and say "Well, whatever happens happens". Many GMs(me included), end up often saying "Well, that didn't go the way I wanted it to at all...it wasn't very satisfying or fun."
If I spent a week coming up with cool puzzles because I want the players to try to solve them and I get satisfaction from seeing their process as they come up with the solutions to them....then any storyline that sees them bypassing all of the puzzles is one that makes me unhappy.