NFL needs to get rid of kickers not change the PAT or goalposts

To make the PAT and field goal less of a sure thing I would eliminate the kicker and punters by instituting this rule.

The player who attempts a PAT or field goal or who punts must be a player who was on the field for the kicking team on the previous play.

So when they score a touchdown you are not allowed to have a person kick who was not on the field for the TD.

For field goals and punts the person who attempts the field goal or punt must be a person who was on the field the previous play. Now if they there is a turn over and the recovering team wants to attempt a field goal or even punt the ball the kicker must be someone who was on the defensive team when the all was recovered or intercepted.

The only time the rule will not apply is for the kickoff that starts the first half and second half. During the game after a team scores a field goal or TD the kicking team must use someone who was on the field for the field goal or touchdown. For Safeties the rule applies as well.

I would also widen the goal posts and have kickoffs from the 35 like they used to.