-1 I know this is contrary to popular knowledge but the gemara calls it a lav hanituk l'aseh and if I recall correctly the chasam sofer paskens not to do it unless you need the eggs
You are correct that the Chasam sofer in Shu"t Oc"h 100 strongly
implies that the mitzvah should only be done if one has a use of the chicks,eggs or some other need for the mitzva (-segula??), and to do it stam lishma may be achzorios.
But this is contrary to the opinions of most of the Achronim and against the established custom. In the various books on the topic many gedolay yisroel are pictured doing the mitzvah while they surely had no use for the eggs.
It is though intellectual dishonesty IMHO on behalf of the sefer "shaleach teshalach" to not even mention or allude to this mahalach of the Chasam sofer though....