You can apply certainly but here is the key. Most execs with good experience all tend to know the same stuff. What makes a board of directors bring on a new ceo and just about most execs for that matter, is what income they will bring in. Generally a ceo has good connections with other companies and can bring in partnerships, customers just by being hired. Sometimes that is more important than actual capability. Relationships with other execs in other companies is a biggy.
Generally speaking if they dont deliver what the board hoped they will find someone else. They tend to get swapped out frequently.