And somehow all of that never addressed the original question... is it not the case that in typical usages of asymmetric approaches that you see larger keys?
Still not getting it. If algorithms using symmetric keys are faster, then for the same amount of time you could afford to use a *longer* key. Also, why can you have public key systems that use DES or DES-like transforms as the core of the message encryption? If DES-style bit manipulations are fast enough for a symmetric key, what made it all of a sudden hugely slow for an asymmetric key? An extra mod'ing of the bits at the right point between the symbol swaps isn't that big of a deal.
In shifting from symmetric to asymmetric keys, aren't you simply shifting from encrypting with a key that provides its own inverse to instead using a key whose inverse is determined by a harder-to-compute congruence relationship? You only compute that relationship once when generating the keys, so for a fix key length and known keys, the performance difference should be on the order of single-digit percentages (as in communications/IO bandwith variability should be more of a factor, e.g. when using spread spectrum in a noisy environment). Creating the key pairs is very slow, but using them isn't intrinsically slow, only particular choices of public key infrastructure implementation.
This position only makese sense if you believe that asymmetric approaches to encryption have to be intrinsically slower than DES in order to encrypt the bits. I worked on one of these beasties once. Such definitely wasn't the case. There are definitely very strong encryption algorithms that you may choose to use that definitely are slow in software, and I vaguely recall one family of them out of UoWaterloo that were non-RSA based yet would involve asymmetric keys being strong+slow, but holding all other variables in the problem equal, simply choosing symmetric versus asymmetric keys doesn't universally change performance in a huge way. The schemes for managing keys and the schemes for encrypting the messages themselves influence performance... but even for DES with private keys that has been true for over 20 years. Different DES variants have tradeoffs between performance, encryption strength via controlling the # of iterations, and recovery to communications noise bursts. The extra features influence the performance, the length of key influences the performance, but the choice of symmetric vs asymmetric key for a specified length doesn't have to change it materially.