I never even thought of that, great point. Let's say it had to be retaken because of something the taker did, would they allow someone else to take it in that case?
Do you mean like if they stuttered too much, or something like that? If they scored then yeah, make them retake it, same player. Maybe even just take the penalty away from the team completely, although you're really opening a can of worms there...
If they miss then it's a miss, would be unfair on the GK to give the taker a second chance.
They'd never make the player retake it if they scored, no matter how far a keeper came off the line. Some people might argue that it puts extra pressure on the taker the second time around, which I guess is the only argument I can see for letting them change the taker. I think it's a poor one though, especially using that farce last night as an example.