Exactly. With a proper lexical order you can search efficiently. A composite index that starts with a month would be useful for finding entries with the given m

Exactly. With a proper lexical order you can search efficiently. A composite index that starts with a month would be useful for finding entries with the given month, but usually we want to find entries recursively, starting with a year, then the month, then the day, if necessary, as at that point we may have already found what we are looking for.