Not really a right or a wrong answer regarding the quick-taking of free kicks - it's just a call you make at the time.
For me, anywhere near the box where the "quick" free kick is a shot on goal, I'm standing over the ball and doing the ceremonial.
I get the whole "it's about the team who've been disadvantaged by being fouled" angle but, in reality, they're not going to get the advantage of their "free kick expert" being able to line up his shot, plot his trajectory, where he's going to place/bend/lift the ball into the goal and all without his run-up being impeded by either a moving ball or a defender right on top off him as he brings his leg back to shoot whilst the ball is in open play. Sure, he's got to circumvent the wall, but in the grand scheme of things, with a direct shot at goal, there's little difference in the "advantage" stakes.
A quickly taken shot at goal after the whistle has gone is simply taking advantage of a goalkeeper being caught unawares or even actually exploiting the fact that everybody is now expecting a ceremonial one. I know there's no law against it, but I'm making life easier for everybody (including me) by doing what the game expects.