Isn’t another aspect of it that it’s sufficiently random / unrecognizable, for example?

I’m very much aware of the differences between symmetric and asymmetric encryption, and realize that symmetric encryption is much simpler, but I figure that if there are weaknesses to be found in algorithms such as md5, then surely there are also potential weaknesses in symmetric encryption algorithms?

Now I’m not saying that this would be the case for battle tested algorithms like AES. But is there any particular reason why this whole category could not possibly have weaknesses?