"Classical," as a historical term, absolutely encodes a judgment not just about the value of ancient Greek and Roman cultures but about the value of specific periods within the history of those cultures. The same can be said for other periodizing terms such as "Archaic" (implying inferiority to the following period) and "Hellenistic" (implying a culture that was Greek-like but not really Greek). These judgments have a long history behind them. Their roots can be traced as far back as Roman reactions to Greek literature, art, and philosophy, but our modern terminology draws much of its force from western European elite ideologies of the eighteenth and nineteenth centuries which chose to idolize certain aspects of ancient Greek and Roman history.

There is a movement among historians, archaeologists, art historians, and others who study the cultures of the ancient Mediterranean to move the field away from terms like "Classical" and "Classics." There is, however, a strong institutional inertia in favor of retaining "Classical" and related terms which makes changing this term harder than discarding "Dark Ages."

Some of this inertia comes from simple familiarity: there is several centuries worth of scholarship that uses this terminology for periodization, and "Classics" is even the conventional name for the study of ancient Greek and Latin languages and literature. (There weren't Departments of Dark Age Studies in universities around the globe that had to get new letterhead.) Some of it comes from the lingering effects of the eighteenth- and nineteenth-century's hero worship of select elements, moments, and figures from Greek and Roman history (what I have elsewhere called the Victorian hangover). Some of it stems from the fact that, as you rightly note, it's harder to find the urgency behind changing a term that sounds positive, like "Classical," than one that sounds negative, like "Dark Ages."

The biggest obstacle to a change in terminology, though, is that the movement to rename elements of the discipline is not just about a change of terminology, but a rethinking of our approach to the ancient Mediterranean as a whole. When we say that we shouldn't talk about ancient Greece and Rome as "Classical" civilizations or that their literature should not be grouped under the title of "Classics," we're saying that we should not privilege the history and culture of ancient Greece and Rome above other histories but rather see them as part of a rich, complex, and interconnected ancient Mediterranean world. That shift is more than a change of terms but a challenge to generations of thought and scholarship, which is a hard thing to do.