The date was chosen to prevent precisely this situation. Prior to 1276, the law was whatever the king said it was at any moment. The idea of the introduction of the "common law" was to provide a proper legal system with courts and the like. They wanted people to be able to use the new courts to deal with relatively recent disputes, but not ancient ones. They therefore chose the date, the beginning of the reign of Richard I, as the cutoff date (which was 87 years prior). Anything that happened in that time period could be brought before the courts, including "yesterday", but anything older was in "time immemorial", so could not.