While some species of trees have evolved to survive fire, such as Douglas Fir and several other conifers, the Bristle Cone Pine is the only one I know of that depends upon fire to open the cones.
There is some misinformation on this page. Fire is the ultimate enemy of Redwood Trees, they have not evolved to survive fires. They survive in only 3 spots in the world where there is lots of fog to provide moisture that protects them. Once they covered the entire earth, but change of climate reduced the fog and moisture and that made them susceptible to fire and reduced them to just the 3 spots they survive in.
Neither species of Redwood Trees, neither S. sempervirens or S. giganteum require fire to open the cones and let the seeds fall. Each Redwood tree will produce between 6 and 8 million seeds each year of which only a few are fertile and will grow. Most Redwood propagation is from new trees growing from buds on the branches and roots of old trees. The "Family Tree" at Jediah State Park on the Ore. / Calif. border is the best example of natural propagation, one can see many trees growing from the branches and above ground roots of the parent tree.
Lodge pole pine is another species that does not require fire. The pine cones open when the dry summer removes the moisture from the cones making them curl and drop their seeds. Lodge pole contains lots of pitch which is like throwing gas on a fire. Letting a lodge pole forest burn will result in destruction of the entire forest.
There is no one solution fits every forest. Some forest could burn and successfully recover, some forest will take thousands of years to recover if allowed to burn. The "Biscuit" fire in Southern Oregon is one that was allowed to burn when it should have been extinguished. The result is the ground is sterilized and won't support trees again for hundreds of years. Fire plans need to fit the individual forest.