In general, my answer would be “do you trust your builder”? If you are purchasing an existing home and aren’t working with the builder, then I would err on the side of caution and hire an inspector before making the purchase. If you are working with a builder that you trust, it shouldn’t be necessary, but also not a problem if it gives you peace of mind. The caveat is that you need to find an inspector who genuinely wants to help. They do exist, however there are also many out there that try to justify their fee by searching for insignificant things. When this happens on an existing home it can scare a potential buyer away or leave them thinking there is a lot to fix, when really there may not be much to address at all. When this happens during construction, it can create an adversarial relationship between the builder and client and then nobody wins, except for the inspector.
Much of what a private inspector notes are either purely cosmetic, already being handled by the builder, or required by local code inspectors. With existing homes, it is common for inspectors to point out items that don’t meet current code. That is fine for the inspector to point out such items to educate you, but don’t expect a seller to update their home to current code, only to what the codes were when it was built.
I welcome “the right” inspectors. Much like with city or county building inspectors, we don’t view the relationship as adversarial. We all should be on the same team, with the same goal, being a beautiful home, built to high standards. None of us are perfect and sometimes potential problems are overlooked or missed and it can be beneficial to have another set of eyes inspecting the work that is working as part of the team. If you choose to hire an independent inspector, make sure they are helping, not hurting the process.