if shibas are doges and corgis are corgis, would a mix of them be called dorge?

Horgi Husky/Malamute + Corgi = top tier doge

As cute as that may be, I really fear for that poor pup's later life. I've heard that Corgis and Shibas both have enough complications of their own due to breeding so cross-breeding between them seems like it's bound to end up badly.

It's because of stuff like that that I always go with a Border Coli. Smart, hard-working sheepdogs. Healthy, long-lived, and plenty of fun.

ACTUALLY, cross breeding usually helps more than it hurts (in most cases anyways). Purebreeds are usually the ones that experience the most problems because of selective breeding weakening the breed rather than strengthening the breed. Crossbreeding "can" give the strengths of both breeds and reduce the likelihood of problems.

Mixing two different kinds of dogs is good for their health.

A dog of each race gets gentic disorders because in order to make it look the way it does its ancestors have been bred only with other similar dogs, narrowing the genetic pool to the point where it started to work like inbreeding. And, as we know, the more inbred a kid is, the bigger chance of it being retarded.

Different dog races means different genetic pools and a mix should actually have much less potential for disorders typical to the races it originated from. It's technically a mutt, only a pretty-looking one.

Long story short, nastoy is correct.

Will variation is the only way to actually fix a lot of the problems.

Well*
God damnit...

It entirely depends what the health condition is about, I suppose.
Bigger dogs cross-bred with smaller dogs can lose the future strain on their hearts and organs because of their other genetic half.

That said, I had a German/Collie mix. Old man lived until he was about 15, nearly 16, and could've probably kept going if he didn't lose his back legs to Shepherd's Arthritis. The Collie mix kept him going remarkably well though past anyone else his age.

Corgi ftw!
corgiorgy.com/

I want one