The reason you need "of" before "crucial importance" is that an adjective is needed to fill the blank in "They are __________ to life" "Importance" is a noun, not an adjective. If you had used "important" (an adjective) instead, you could have omitted "of": "They are crucially important to life" However, to use the noun it is necessary to transform it somehow into an adjective. To do that, you create the adjective clause "of crucial importance" that behaves as an adjective. You can use this clause to replace an adjective in any sentence: "He is happy" (adjective) "He is of crucial importance" (adjective clause) "That is a big building" (adjective) "That is a building of crucial importance" (adjective clause)

It doesn't add the 'of' before 'they are'.