That's fine, but that was not your original point which I was picking at. Your point was: I want to fire Karl regardless whether we make the playoffs because he won't change his style, and doing so will not allow us to make the playoffs (unless by "make it" you meant "winning a championship").
As to your point, I don't see Karl as a long-term coach who's going to be coaching us to multiple championships if that were even possible. His age is a very real concern. That said, IF he makes the playoffs this season then regardless of style or whatever I think you need to keep him. You fire the coach who just got the franchise it's first playoff shot in 10 years in what would be an incredible second-half turnaround and it would just solidify the franchise's position as the laughing stock of the league. Fans here may not think much of Karl these days but I doubt that's the case in the coaching community. No legitimate established coach would be willing to come here, nor would any big time FA, and your only shot would be at finding a Mike Malone/ Brad Stevens (young coach ...) and giving it another 2-3 years for the team to get it together and learn a new system etc. Keep Karl, make another playoff run next year, and if we're still just a fringe playoff team barely securing the 8th seed then you can consider firing him instead of keeping him for what I think would be the last year of his contract. If we're a solid playoff team, I see no reason not to keep him for another year, even if we're a 1st round exit, which in and of itself shouldn't be a measure as to how well we're doing. A franchise out of the playoffs for as long as we have shouldn't expect to be making championship runs in its first 2 seasons of making the playoffs. Regardless, you have a team that has been to the playoffs twice under Karl, has more experience winning and if as it turns out as you so strongly believe, that Karl cannot win in the playoffs, then it will be obvious and you can hire a new coach to make the necessary adjustments for a serious championship run. You'd have a core in place that has experience in the playoffs playing together, and so making those adjustments will be far easier.
There's no such thing as not having a culture of winning when you're winning. Winning under Karl in itself builds a culture of wining. I'm not too interested in "winning the right way" at this point when we're 10 years out of the playoffs and an abysmal franchise all around.