A common problem that comes up in exercise is muscle imbalance. One side of the body may be stronger than the other in certain lifts. Obviously, it's better to have more symmetry in terms of muslce power if possible.
The usual advice is to work on form, making sure that both sides of the body are working equally on a lift. Also, a person may be advised to do isolation exercises to strengthen the weaker side.
I had a different thought on this. I wonder if muscle imbalances can be caused by always lifting symmetrical weights. For example, if you deadlift 100 pounds, then the weight is evenly distributed across the bar. However, our hunter-gatherer ancestors never lifted such "perfect" weights. They instead lifted odd-shaped rocks, carcasses, etc.
I will use the analogy of running. If you always run on a flat, perfectly smooth surface, then you never develop the little muscles that help to achieve balance when on an irregular surface like a trail. In the same way, maybe always lifting symmetrical objects never allows complete muscular development of each side of the body.
One concern that may come up is the potential danger with lifting irregular-shaped objects. I'm not sure on this, but I do know that if you stick with real objects (like rocks), than you won't be able to lift tons of weight anyways. I'm sure if a person tries an unbalanced 400 pound barbell deadlift that they might be setting themselves up for trouble. However, if a person picks up an odd-shaped heavy rock then maybe there is only minimal risk.
All of this is just a hunch. I know of no research that shows picking up irregular objects is beneficial. It wouldn't surprise me though. It seems like lifting an irregular object would be more of a "complete" lift than picking up a perfectly balanced weight.