Very good question,specially in aerospace supply chain senario.If your position is at lower tiers in supply chain your products will be as per your customer requirements so setting quality objectives by you for your products may be a violation of requirements and a risk.
However,if you consider about aircraft or engine manufacturers,you would agree that they are continuously attempting to improve their products in terms of features,reliability,efficiency,safety--------------.
Once it is set as objective the requirements are transferred to suppliers in supply chain line.
Are you worried about this point for the audit?Many auditors have not noticed/overlook that there is a requirement of "quality objectives for product" in clause 5.4.1 too
and the requirement of planning in 7.1 is to meet those.