Doesn't work for things we know are exponentially faster on quantum computers. Eventually, with enough (but not an absurd number) of bits, a decent quantum computer can solve problems that wouldn't be possible on a classical computer the size of the universe operating for billions of years.
Improvements in algorithms cuts both ways, too. And for some classes of problems, it's possible to prove (given P != NP, etc) that any classical algorithm is much worse than quantum.
In short, it's hard to classically model pretty simple quantum mechanical systems and sample the probability distribution of outcomes. Using a quantum computer to simulate the system and sample the probability distribution is easy.
IIUC and IIRC (both somewhat doubtful admittedly), Feynman argued - https://people.eecs.berkeley.edu/~christos/classics/Feynman.... - that only a quantum computer can perform a scalable simulation of quantum physics. Assuming that is correct, there is no option for "traditional computers" to catch up for all problems at least.
What I mean by traditional computers catching up with it is that we will see innovations in traditional algorithms that either make quantum computers extremely pricey for a very long time in respect to traditional computers or that we find innovations that will bypass the things that they are good at without violating any of the current theories we have.
Currently, we have an enormous effort invested in our silicon architecture. We seem to be hitting limitations to silicon and they seem to be making a large bet on Quantum computers to eventually allow them to proceed. But, if quantum algorithms take a long time to have useful implementations then we have a local maxima where quantum computers aren't close enough to implement without investing a massive amount of money and that silicon just becomes cheaper and cheaper. When Intel finally reaches the limit of traditional computing that doesn't mean that it won't stop being cheaper.
Intel, IBM, Microsoft, DWave, Google and other companies have small bets on quantum computer engineering strategies that may or may not pay off. Also there seems to be a bunch of researchers publishing more and more papers on the theory of quantum algorithms. There are cross collaborations with academia on quantum computation (and they are basically what the research institutions work with the quantum engineering departments in those companies).
If we find that quantum computers can only speed up computations in the limited set of algorithms then they will probably end up as accelerator cards attached to traditional computers. I expect a order of magnitude of inefficiency to translate problems or do work on quantum computers. Either due to interconnecting or the way that we will figure out to operate them. So we will see these systems relegated to supercomputer workloads.
On the algorithms side, funding the research of quantum algorithms will probably dry up in the way that string theory research has.
Hopefully we will see a large breakthrough that will make quantum computers feasible. From my reading of the research it seems like Topological Quantum Computers have the best chance.