I've been thinking about this and I have a few comments to make about it. I will first preface this with a comment that I am not focused on the House of Habsburg, the Holy Roman Empire, the Austrian, or Austro-Hungarian Empires, but as a French focus there is constant interaction with the two.

The Habsburgs are for lack of a better word, hasbeens. Due to the shifting of power in Europe away from the Habsburgs in the 15th and 16th centuries to France and Britain, the excessive destruction and pain of the 30 Years War, and a slow irrelevancy in European affairs from the lost of major holdings (Spain in the War of Spanish Succession and Silesia in the War of the Austrian Succession), the Habsburgs are effectively pushed out of importance. By the 19th century, they become a second rate power, losing importance to Prussia/Germany and Russia.

After the loss of importance, there's another issue, and that's of multiculturalism. This isn't to say that it is bad, but due to the composition of the Habsburg realms, there is no such thing as a standard citizen. Under Habsburg rule in the years before WW1, the Austro Hungarian Empire claimed Austrian-Germans, Czechs, Slovaks, Polish, Hungarians, the odd Italian, Croats, Bosnians, and more other ethnic groups that I cannot think of right now. There is no proper unity like that in Germany, France, Italy, Britain, or Spain, with Britain the only of those that didn't have any land once in Habsburg. With a multiethnic empire that balkanized after the Great War, you no longer had a single Austro-Hungarian nation but a multitude of nations that claimed independence. Now you have multiple nations of a variety of ethnic and linguistic claims. Combine that with an American culture (as I cannot speak about British culture but I will agree that the Austro-Hungarian Empire is rather under represented in Anglophone history) that has a near obsession of saying "my ancestors are X", you develop something where the smaller ethnic identity is more important than the larger hodgepodge of ethnic groups under a single empire.

I would like to point to victory, and the lack thereof. Pop culture and pop history loves warfare, but battles with famous characters that led troops to victory against all odds, more so when gunpowder becomes introduced. Within the time period I focus in, I can only name Wallenstein, Archduke Charles, and Swharzenburg as major commanders. Britain, Germany, France, and Russia have more games commanders than the Habsburgs had titles. So perhaps a major point of the lack of Habsburg representation is that, they just aren't interesting as a popular historical subject. We like victory, we like drama and passion, we wouldn't want to talk about a "nation" that defeated itself in a battle.

Finally, there's the matter of what you asked. You ask about the Habsburgs, a family long famous for marrying well. That's effectively the problem, they are a family that married well. Sure they had importance in politics and diplomacy but they were a family that married well and held titles that are easily separated from their lands. With the exception of the Archduchy of Austria, the Habsburgs lose anything that is connected to them. They aren't tied to a nationalist narrative or see a nation enter the Modern era. They see a multiethnic empire fall apart into a multitude of countries.

None of this is bad, history simply played itself that the Habsburgs found themselves irrelevant.