As Singh indicates in his The Code Book, the Beale Ciphers have gone unbroken for over a hundred years, the best and brightest minds of recent decades pouring hours upon hours into the effort of deciphering them. Unfortunately, their work, as of yet, has borne no fruit. Ultimately, this begs the question: why do people continue to attempt that which has eluded the brightest minds of this generation and those long since passed?
I believe the answer is twofold. Of course, money is a key motivating factor. $20 million by today's standards is quite a bot of cash, and would enable an individual to live quite comfortably for the rest of their days. In fact, as Singh points out, there are entire societies that have been formed around the goal of solving the Beale Ciphers, their membership contingent on how the treasure, should it be discovered, would be allocated to the members of said society; often, the people who crack the cipher believe they should have the right to keep all of it. For that reason, it is impossible not to acknowledge money and, by extension, greed, as one of the key motivators that drives people to crack the Beale Cipher.
Beyond that, however, lie the intellectuals, those who see the Beale Ciphers as the ultimate challenge, akin to winning a Nobel Prize or Fields Medal. For them, the money is irrelevant, as the Beale Ciphers serve as the perfect opportunity to affirm their skills as cryptanalysts and codebreakers. These people are likely driven by pure intellectual curiosity, much like Babbage and Poe, wanting to test their abilities against the hardest cryptographic problem the world has yet to offer. For that reason, their motivation for solving the Beale Ciphers is akin to that of George Mallory's for climbing Mount Everest: because they're there, they must be solved.