In a word, no. MLB should not do anything at all. This strikeout situation (I'd call it an epidemic!) lies in the decisions hitters are making or not making. Strikeouts are at an all time high because hitters are being taught :
1) to come out of their cleats and swing for the fences even with two strikes. The idea of choking up, and putting a ball in play is absolutely foreign in todays professional game.
2) hit the lower half of the ball to impart a launch angle. So not only do they want athletes to do one of the hardest things in all of sports (hit a fast moving ball that has spin) but they want you to hit the lower half of the ball. Good luck with that at any level!
Possibly MLB could publish and distribute a pamphlet on swing reduction and hitting line drives to better help their hitters.
PS...I was watching an MLB game the other day. The infield had shifted entirely to the right side. There were 4 IFs from 2nd based to 1st base. They were giving this guy a bunt single to any place on the left side of the infield. He wouldn't take it. He struck out looking. That in a nutshell is what is wrong with hitters in todays professional game.
The game is perfect the way it is, it just needs smarter players willing to do things to help their team.
As always, JMO