The pasuk describes the bigdei kehunah as “l’kavod u’l’tiferes”, something which adorns and brings honor to the wearer. The Lev Sameiach writes that had the Ramban been right that bigdei kehunah are not an independent mitzvah but just a necessary ingredient to performing avodahm their function should have been described as “l’amod u’l’shreis”.
Be that as it may, the Ramban in his commentary to the Torah writes on “l’kavod ul’tiferes” that the bigdei kehunah had to be made lishma, with the proper kavanah that these garments would be used as bigdei kehunah. The Rambam, as the Minchas Chinuch notes, nowhere cites such a requirement. (The point seems to be a machlokes in the Yerushalmi).
This is pure speculation which may not make sense, but perhaps this machlokes is also l’shitasam. If bigdei kehunah are a hechsher mitzvah to avodah, perhaps they take on the requirement of lishma just like avodah itself. But if it is an independent mitzvah, like the Rambam holds, the requirements need not match.