Proficiency in the Olympic lifts (snatch, clean, and jerk) is not an indicator of fitness. You don’t have to perform them to be in peak physical shape.
In fact, some people should stay away from certain lifts. For instance, people with certain shoulder issues shouldn’t snatch.
The Olympic lifts are complicated movements but taught properly are safe (as long as you are free of injury and move well), fun to learn, and challenging to perfect.
There are some great benefits, including:
For most people, the Olympic lifts don’t actually make you stronger. This is because they are technique-dependent, so it’s hard to go heavy enough to actually build strength.
Want to increase your Olympic lifts? Get stronger in squatting, pressing, pulling off the floor, and generating power and speed. Get REALLY GOOD at the technique of the Olympic lifts and, over time, you will be able to lift more in the snatch, clean, and jerk.
Some caveats:
Again, your approach should be to challenge yourself on traditional weight lifting (squat, press, pull, etc.) to build strength while going light to moderate on the Olympic lifts, striving for perfection (hitting each position, receiving the bar properly, etc.), improving timing and engraining the proper technique. When you go too heavy with an incorrect technique, you are only promoting that substandard movement pattern. No one likes an ugly snatch, am I right?!
So, make it pretty!