Based on the documentation initialDelaySeconds gives some delay before the first readiness probe is checking the pod. But the only effect of readiness probe failure is that the pod is marked unready: Does not get traffic from services and also affects the deployment state.
So giving readiness checks some delay is not really effective for the majority of the applications: We want to make the pod early as soon as we can, meaning we need to check if it's ready as soon as possible.