I didn't read the whole thread, so I don't know if anyone else mentioned this.
Enterprise is not a thing, or an individual. By definition, "Enterprise" means "a project or complex undertaking".
So it's correct to call it "The Enterprise" because it's referring to a collection of processes to create something.
The whole idea that "The Enterprise" means "The undertaking of humanity to explore the unknown".
Voyager on the other hand, is an individual. A "Voyager" is an individual who goes to explore or travel to a different location.
Calling it "The Voyager" doesn't really make sense, although it can still be used, just sounds redundant.
Calling the Enterprise "Enterprise" is trying to turn the word into having a singular meaning, like it's a person or a thing rather than an idea. It would be like instead of saying "The Undertaking", to say "Undertaking"
I hated every time I heard "we're taking Enterprise somewhere"
I feel sorry for the cast.