No. Absolutely not. You want players willing to step up and have the balls to take one even after he's just missed the last 2. You get no personal glory from scoring penalties, everybody expects you to score, you can only fail.
Pep chooses the penalty takers, he's decided Mahrez is still second best option, I'd be disappointed if any player would hide away from taking one, it shows a weak mentality.
Sterling is probably the worst penalty taker in terms of technique I've ever seen from a professional footballer but I always admired his willingness and mental strength to continually want to take them.