The arms race already exists: hash sizes and standard key sizes have increased. Because Moore's Law already applies to classical computers: you effectively lose 1 bit of entropy / security every year.
Moore's law refers to hardware capacity and not speed. If you can't figure out how to completely parallelize your attack then that is important. And things are not getting significantly faster.
So a lot of stuff is likely to be safe indefinitely under current technological conditions. A complete breakthrough like quantum computing would be required. Makes it hard to predict things.