It's not really that different from "Europe", especially when you listen to Americans talk about "Europe".

Yes though Europe is a lot more culturally similar and has a shared government for the most part.

Asia has very distinct countries and in some cases is even at war even if it's a cold one. Like India vs Pakistan, India vs China, North vs South Korea, China vs Taiwan. And customs, languages and (where applicable) religions are more radically different than within Europe too.

It makes less sense calling it "Asia" than it is calling Europe "Europe" :)

At least in the case of "europe" it could refer to the EU (which obviously is not correct because it doesn't encompass all of europe). But when they are talking about "Asia"—what governing body would they even be referring to? It's obviously non-sensical.