I think a large part of it is that chemistry, for the most part, tends to focus a lot on what is, essentially, a single branch of physics. As a result you get lots of papers about creating a new chemical, or about the properties of a new chemical, but the fact that the majority of them have long, latin names and the fact that many applications aren't immediately apparent means that it just isn't interesting to the common person that much.
By that logic, biology is simply a single branch of chemistry. But as to the applicability, that just means we're failing to communicate what we are doing effectively. A large number of us are making very useful products. I'm trying to make bio-renewable and bio-degradable plastics out of corn with high glass transition temperatures. I know people who make anti- testicular cancer drugs that cost ~1/100th of current drugs and are ten times as effective, somebody working on vaccines against drug use, somebody working on chemotherapy delivery systems that will minimize the impact on off-target organs, and the list goes on and on.
That's also probably why even when chemistry does make the news it's almost always the applications of it while skipping over the process. You might see a headline like "NEW FUEL CREATED", but you aren't going to see one like "NEW PROPERTIES OF AMMONIA DIHYDRALE METHALATE FOUND" (just made that name up out of the blue, probably doesn't even exist).
I don't know that this is a problem. I'd be happy even if I saw more headlines like the first that actually recognized that chemists did it.
Even the basic parts of chemistry are rather esoteric. Just learning the basis of a chemical reaction requires you to be able to look at and understand a rather large chart of different elements, understand how valence electrons work, etc.. Physics, on the other hand, is basically doesn't suffer from either of those problems. The basics of physics can usually be drawn fairly well from analogy, which makes them easy to explain to those not in the know. In addition the results are usually things that people have been experiencing all their life, and as such are immediately apparent.
I think this just means we're failing to find appropriate analogies. I think chemistry could make the same intuitive sense, but most of us are just better researchers than educators.
As an example if I was trying to teach someone the basics of how light works I might be able to draw examples of things like rainbows and mirrors that people work with in every day life. On the other hand pretty much all of the chemistry examples you meet in ordinary life fall under a different heading, "cooking". If I was talking about light I could speak about how you can do a variety of different things to light, like bending it, splitting it, combining it, reflecting it, and what exactly was happening in each case and how they made different things happen. In chemistry you're largely confined to "we mix X and Y and Z in a big pot, heat it to this temperature, and wait for a while to get W".
That's fair, but there are ideas beyond mixing things which we could attempt to explain, i.e. stereochemistry, conjugated pi systems, aromatics, functional groups in general.
In physics we already know the applications, so the reasons why they happen are cool but still simple enough to be understood. In chemistry the reasons are mostly the same, and they're complex enough to not be easily understood, while the applications tend to either be so esoteric nobody but chemists can see them, or they are so big they overshadow the chemistry part itself. And all the simpler, common chemistry things don't even get known as chemistry, they get thrown about into other fields like cooking.
I think this ties back both into the fact that chemistry is in more than is recognized, and we need better analogies. I appreciate you sharing your experience with chemistry.