Does pairings based cryptography inherently require a CRS/trusted setup?
No. For example, these pairing-based protocols don't require trusted setup:

BLS signatures;
tripartite Diffie-Hellman, as mentioned in Elias' answer;
some identity-based encryption schemes (when users are their own PKGs, e.g. when using IBE for forward-secure encryption);
the Bünz–Maller–Mishra–Vesely polynomial commitment scheme. (This could in principle be used for NIZK arguments of knowledge, although it has $\Theta(\sqrt{N})$ verification and so is not fully succinct.)