Blowing small issues out of proportion is a favored hobby on SE. ;)
I've thought about this a fair amount, given some recent interest in the topic, and I think we've run into an etymological problem more than a culinary one. There are many cases where things get assigned a name based on usage, common settings, or common features, that disagrees with the name you would assign it from a purely taxological position. Common examples would be: Whales were called "fish" for many years. Tomatoes are botanically fruits, but are commonly referred to as a vegetable (as are eggplants, peppers, etc.). Cheesecake is called "cake", when structurally it is clearly a custard pie.
In the case of quickbread/cake, I think the problem comes down to the fact that, while many cakes use chemical leavening, they weren't invented because of chemical leavening.
As far as I can tell, the prototypical "quickbreads", such as muffins, scones, soda-bread, American-style biscuits, banana bread, etc., were invented largely because of the existence of baking powder. Certainly people made foods like this before that, but using only natural leavening or no leavening would leave them very different from the modern versions.
These breads share a common trigger, and some common features. They are all relatively low fat, relatively low sugar, they do not rely on the formation of gluten to build structure (yet, historically, are typically made with moderate protein all-purpose flours), and even when they do have fats and sugars, they do not rely on them to inhibit the development of gluten in a specific way (as in a pastry), instead, they all share the "muffin method" of mixing wet and dry ingredients separately, then combining, mixing quickly, then immediately baking.
Cakes, on the other hand, have been using other forms of air-introduction for a long time. Think about the traditional pound cake, which uses air trapped when butter crystals are creamed with sugar. Traditional recipes call for you to cream the butter and sugar together for hours and hours to get enough air in (easy when you have servants). Angel food cakes use beat egg whites to get sufficient air into the mixture. Most use low protein cake flour and high fat content to prevent the formation of gluten, meaning the "muffin method" of mixing is not commonly used.
These cakes were not invented to rely on chemical leavening, even though they took advantage of it once it was invented. Modern cake-in-a-box is much like a quickbread in that it uses 100% chemical leavening, but it uses low protein flour to prevent the formation of gluten during mixing, and it wasn't really "born" to use chemical leavening - its closest ancestors didn't need it. I could bake you a number of delicious cakes without the use of baking powder, but it is such a convenient tool for a more reliable boost that it is very commonly used.
In conclusion, while modern quick breads and many modern cakes share many recipe details, they don't register as the same thing in people's minds because of their different histories, and some details about their construction. They arrived at a similar place through convergent evolution, not because they are closely related to each other. Language isn't just about accurate description and taxonomy, it is about history, intent, and a associations. I can't begrudge people for not calling cake "quickbread", not calling a pepper "fruit", or not calling Cheesecake "New York Custard Pie".
- Google N-Gram results showing the rise of terms such as "quick bread", "soda bread" and "banana" bread. All modern inventions.
- Google N-Gram results showing the invention of baking powder in the late 1800's (technically "invented" in 1843, with the most popular double-acting powders reaching the market in the 1880s), culminating with a huge spike in popularity right after 1900.