>Just a basic cryptographic risk management principle that cryptography people get mad at me for saying (because it’s true) is: don’t use asymmetric cryptography unless you absolutely need it. Is there any truth to this? Doesn't basically all Internet traffic rely on the security of (correctly implemented) asymmetric cryptography?
Yes, symmetric cryptography is a lot more straightforward and should be preferred where it is easy to use a shared secret.
> Doesn't basically all Internet traffic rely on the security of (correctly implemented) asymmetric cryptography?
It does. This would come under the "unless you absolutely need it" exception.