Before I start, let's face some facts here, the workout routine optimal for your progression is dependant upon your end goal. Typically weightlifting is broken down into Powerlifting, Bodybuilding and Olympic Lifting. Powerlifting and Olympic Lifting revolve around strength progression and Bodybuilding revolves around muscle progression.
For Bodybuilding the reason an Upper/Lowerbody workout routine is optimal for a natural athlete is simple. It revolves around providing rest to muscle groups that have been worked out within the last 72 hours. Why 72 hours of rest? Protein Synthesis is elevated up to 48-72 hour after heavy resistance training, so your body will experience muscle progression over the duration of this time. It would almost be redundant to workout the same muscle groups within this duration since they will still be rebuilding and it is best to let them recover for your next workout which involves those same muscle groups. For instance, I work out all upper-body muscle groups on a Monday so it is ideal for me to allow all those muscle groups to rebuild during the 72 hour process of elevated Protein Synthesis and have my next upper-body workout on the upcoming Thursday. Below is a good example of an Upper/Lowerbody Split workout.
Bench Press - 5 Sets 5 reps (2 Warmup exclusive sets)
Pedlay Rows - 3 Sets 8-12 Reps
Incline Dumbbell Press - 4 Sets 8-12 Reps
Lat Pull Downs - 3 Sets 10-12 Reps
Cable Lateral Raises - 2 Drop Sets 8-12
Barbell Curls - 2 Drop Sets 8-12 Reps (ArmBlaster)
Tricep Pull-Downs - 2 Drop Sets 8-12 Reps
Deadlifts - 3 Sets 6-8 Reps (2 Warmup exclusive sets)
Leg Press - 3 Sets 8-10 Reps
Hamstring Curls - 3 Sets 8-10 Reps
Standing Calf Raises - 3 Sets 10-12 Reps
Knee Ups - 2 Sets 10-12 Reps
Cable Crunches - 2 Sets 10-12 Reps
Wood Choppers - 2 Sets 10-12 Reps
Pull-Ups - 3 Sets 6-8 Reps
Overhead Press - 3 Sets 6-8 Reps
Seated Cable Rows - 3 Sets 8-10 Reps
Dumbbell Press - 3 Sets 10-12 Reps
Cable Flies - 2 Sets 10-12 Reps
Barbell Curls - 2 Drop Sets 8-12 Reps (ArmBlaster)
Tricep Pull-Downs - 2 Drop Sets 8-12 Reps
Squats - 3 Sets 6-8 Reps (2 Warmup exclusive sets) Front Squats - 3 Sets 8-10 Reps Hamstring Curls - 3 Sets 8-10 Reps Standing Calf Raises - 3 Sets 10-12 Reps Knee Ups - 2 Sets 10-12 Reps Cable Crunches - 2 Sets 10-12 Reps Wood Choppers - 2 Sets 10-12 Reps