Isn't ZKP is a reduction to a hard problem, rather than true zero knowledge?
One of the most basic assumptions in cryptography is the existence of hard problems, even on a very conceptual level. For example, to establish a secure communication channel, you want your cipher to impose problems on eavesdroppers which they cannot solve.

The problem is that the existence of hard problems generally has (severe) impact to questions in complexity theory. The most attractive problems for cryptography are those in $\mathsf{NP}$, in particular because, assuming $\mathsf{NP}$ has intractable problems, these have nice asymmetrical properties: Although you can verify a solution efficiently, it is infeasible to find one. However, establishing intractable problems in $\mathsf{NP}$ necessarily entails proving $\mathsf{P} \neq \mathsf{NP}$.

Furthermore, some cryptographic primitives imply the existence of hard problems even without basing on the hardness of a particular problem. For example, the existence of one-way functions, which are essentially the most basic cryptographic primitive, implies $\mathsf{P} \neq \mathsf{NP}$. We also know one-way functions exist if and only if PRNGs exist, so it is clear one-way functions are not an isolated case (whose existence is hard to establish). Also, asymmetric cryptography implies the existence of either of these primitives. (Read more on Impagliazzo's five worlds if you are interested in these issues.)

Modern cryptography is highly dependent on complexity theory for its assumptions. Since that is the case anyway, it only seems natural to embrace the conjectures of complexity theory too.