Duvidf, you’re being pedantic. For whatever reason, whether it’s the ikar hadin or because of eis la’asos (he adds that possibility even if the ikar hadin is like that Rambam, but seems to hold it actually isn’t) the fact is it’s muttar and therefore proper.
Would you similarly argue that someone who learns Torah sheba’al peh from a sefer is doing something wrong since it’s only muttar because of eis la’asos Lashem heferu?