Yes, Realtors can only recommend, but cannot choose the inspector. That is up to the homebuyer.
And, I agree on getting a three-stage inspection (foundation pour, framing inspection - before drywall is installed, and a final inspection after the property has been signed-off by the city inspectors). Some inspectors will even do a pre-pour inspection. Waiting until the end for your only inspection won't tell you what is behind the walls or beneath the flooring.
And, Rene is correct - most inspectors will also do another warranty inspection before your warranty is up to help you identify any issues that may have arisen since you move into the house. Sometimes those issues are things that should be take care of by the builder/builder's warranty.