It gets even more muddled today with the normal use of statistical contingency fuel. How ICAO arrived at those figures, no idea. I guess it was a rough estimate about the most fuel you usually need in case of some unanticipated circumstances. For all the normal stuff you can plan for you already take fuel after all.
By the way, the 30 or 45 minutes (45 minutes exists for jets as well if you dispatch without an alternate) is not contigenty, it is final reserve. Once the crew knows it will use part of the final reserve fuel it has to declare MAYDAY FUEL, that is, at least in EASA, required by law. By that time the crew will usually have a low fuel warning anyway as they have used up all the other fuel (trip, taxi, contingency, alternate fuel or the 15 minutes holding fuel for the case of no alternate dispatch and any extra fuel the crew might have decided on taking).
Contingency fuel we can use, that is, after all, what it is there for.