How many different viruses are there that cause the common cold? About 200? If we can get an effective vaccine for this coronavirus in under a year why aren't w

How many different viruses are there that cause the common cold? About 200? If we can get an effective vaccine for this coronavirus in under a year why aren't we working on all the other coronaviruses and rhinoviruses? I know nothing about biology but let's say it costs $1 billion to develop and test a successful vaccine for a common cold virus, worldwide for $200 billion that isn't that much to not have to deal with colds anymore. Plus it seems like one vaccine might provide protection for multiple different viruses. Or do they mutate too quickly to keep up?