Worth including the Mt Fuji and Hakone area on a Japan tour, or better to spend longer in Kyoto?

Some itineraries add a night around Hakone for the Mt Fuji views, but I’ve read Fuji spends half its life hidden in cloud - and that time could go to more of Kyoto. We’d hate to gamble a precious day on a maybe. Did Hakone earn its place for you, or would you hand the time back to Kyoto?