Sforno on Numbers 3:3/ספורנו על במדבר ג׳:ג׳

1הכהנים המשוחים, future priests were not described in such terms as they were not anointed while the High Priest was alive. אשר מלא ידם לכהן, the reason why the sons of Aaron were also anointed with the oil of anointment was to enable them to perform priestly duties, as otherwise there would have been no priests other that Aaron, no one having been born as priest to a father who was a priest. Had they been born after Aaron’s appointment, they would not have required such anointing as heredity would have sufficed.