Wendy's did have milkshakes for a while though. As I recall though, the taste was quite different from the frosty, which has me suspecting that the frosty itself isn't ice cream at all, but frozen custard. This would make it a concrete if I was right.
Fun Fact: Wendy's chocolate frosty is actually 50/50 flavored. The first manager thought that chocolate would counter the taste of the burgers, so they blend vanilla flavor into the recipe to temper it. The vanilla frosty itself wasn't even added until 2006 (Over 35 years after its founding).