The most sensational, and arguably most valuable, use is breaking hard encryption, so QC has "nation state STEM/security funding" written all over it. Even if it's 1% likely to be used in this way, it makes sense for wealthy nations to spend on it. But yeah, it's not the same story as for the IC boom.
>Is there anything even a tiny QC can do better, faster, and cheaper than a classical computer?
This is a really good question, and I don't know the answer. If I were to try, I'd focus on QC efficient algorithms, and what you can do with that in an application. So, in your system a QC is a magic box that takes an O(n^2) algo and makes it O(n), say. But for ordinary humans, n is very small, so this won't matter. I don't think there is mundane problem, e.g. one dealing with ordinary productivity, that a QC can do better than classical. It's shaping up to be a nation-state funded capital intensive information superweapon against private communication. And you know what? Maybe if you can maintain the infrastructure and staff to build one, you deserve to have it! It's especially untroubling if it's capacity is limited, like being able to read 10 2048-bit RSA encrypted messages per day. That's a superpower, but a very limited and expensive one, which I am fine with.