>They aren't
>supposed to be stutter stepping or hesitating, you're supposed
>to keep the same pace in your run up, especially once you're a
>certain range/number of strides from the ball.

The laws say otherwise:

https://www.theifab.com/downloads/laws-of-the-game-2021-22-booklet?l=en

2. Offences and sanctions
Once the referee has signalled for a penalty kick to be taken, the kick must be taken; if it is not taken the referee may take disciplinary action before signalling again for the kick to be taken.

If, before the ball is in play, one of the following occurs:
• the player taking the penalty kick or a team-mate offends:
• if the ball enters the goal, the kick is retaken
• if the ball does not enter the goal, the referee stops play and restarts with an indirect free kick except for the following when play will be stopped and restarted with an indirect free kick, regardless of whether or not a goal is scored:
• a penalty kick is kicked backwards
• a team-mate of the identified kicker takes the kick; the referee cautions the player who took the kick
• feinting to kick the ball once the kicker has completed the run-up (feinting in the run-up is permitted); the referee cautions the kicker