What is the point of differential cryptanalysis when the amount of necessary plaintext is unrealistic? As someone with a non-crypto background, I learned that differential cryptanalysis is mostly weak against ciphers like DES because, being a chosen plaintext attack, for a state of art complexity of $2^{47}$ there is a need for $2^{47}$ plaintext bits to conduct this attack which is realistically infeasible.
So what's the point of this attack vector at all? If it has always been known that you need a huge amount of plaintext for these to work, why did people bother?
Differential cryptanalysis is a very powerful technique that permitted highly practical attacks on many ciphers that were not designed to resist it (e.g. FEAL-4).  DES, as it turns out, was designed to be pretty resistant to it, which is why it requires an essentially impractical amount of chosen plaintexts to implement a differential attack on DES.  

However, I would note that $2^{47}$ is still significantly less plaintext than a generic codebook attack requires, and moreover the attack has a time complexity of only about $2^{37}$ DES calls (which is significantly better than the generic key-guessing attack).  As such, differential cryptanalysis counts as a 'break' of the cipher (anything that is better than generic attacks is a 'break').  It is only an 'academic' break, given the impracticality of so much chosen plaintext (which is why DES wasn't immediately deprecated once Biham and Shamir published their paper).  But it is a break nonetheless.

In general, people 'bother' with cryptanalysis because they want to evaluate the ciphers they use to protect lives and billions of dollars against all known attacks in order to understand how secure they are.  If you can show (for a cipher with sufficiently large parameters like key-size and block-size) that nothing beats generic attacks (i.e. that there are no 'breaks') then that gives people confidence in the security of the cipher.