NIST DRBG algorithms' optional parameter
A partial answer is that the 2012 version of SP 800-90A included a fourth DRBG construction, Dual_EC_DRBG (§10.3.1.2), for which the security_strength parameter was required. Since one DRBG flavor required this parameter, to have a common interface, all DRBG flavors had to take this parameter. In Dual_EC_DRBG, security_strength is used only for one thing: to select the curve.


  Using the security_strength and Table 4 in Section 10.3.1, select the smallest
  available curve that has a security strength security_strength. The values for
  seedlen, p, a, b, n, P, Q are determined by the curve.


Dual_EC_DRBG was retired after it became public that is was probably backdoored by NSA, but its legacy survives in this minor way.

What escapes me is why Dual_EC_DRBG chooses the curve based on the security strength, whereas Hash_DRBG and HMAC_DRBG are parametrized by a choice of hash algorithm and CTR_DRBG is parametrized by a choice of block cipher.