I absolutely think that they should. Adding in foam rolling and dynamic stretching before my workouts has been amazing towards preparedness, energy, and injuries have almost become nonexistent. Static stretching afterwards, except for certain lifts I'll go ahead and stretch out what's need. For example for squat I'll stretch hip flexors and hamstrings.
Taking something from The Cube by Brandon Lily a good pre-workout routine is:
stretch (rotators, it bands, hip flexors, etc.)
warm up (a movement akin to what your main lift will be)
Doing these things have done wonders for me personally.
"...I have found the Iron to be my greatest friend. It never freaks out on me, never runs. Friends may come and go. But two hundred pounds is always two hundred pounds." - Henry Rollins