Is there any IND-CPA secure stream cipher with a "standard" hardness assumption?
Sure.

one-way permutation ​ + ​ strong hard-core functions
$\to$
pseudorandom generator
$\to$
stream cipher

The keystream is concatenation of the strong hard-core function's values at

the iterates of the one-way permutation on the key. ​ ( k,f(k),f(f(k)),f(f(f(k))),... )