There is a minhag, a predominantly ashkenazc diaspora one, to only do Birkat Kohanim on Yom Tov. My question is what is the Heter for this? There is a general principle we don’t pass up mitzvot when we have the opportunity and they won’t burden us, why would this be any different?
R Ari Henkin (here) brings two reasons for the custom you mention
There are a number of reasons why Ashkenazi congregations in the Diaspora only perform Birkat Kohanim on Yom Tov. The most celebrated answer is that a Kohen is only permitted to perform the Birkat Kohanim when he is happy. It is taught that Jews in the Diaspora are never truly happy due to the many social, financial, and political pressures that are characteristic of life in the Diaspora. So too, no Jew can be truly happy living in Exile, far away from his God-given homeland. Even on Shabbat most people are distracted by their weekday pursuits and worries, and are not fully at peace. On Yom Tov, however, people are in a more festive mood, especially during the Mussaf service. As such, the custom evolved to only perform Birkat Kohanim on Yom Tov. (Rema, OC 128:44)
Another explanation offered for only performing Birkat Kohanim on Yom Tov is that it is preferable, if possible, for Birkat Kohanim to be performed by a Kohen who has recently immersed in a mikva. Since most people don’t immerse in a mikva on a daily basis, or even Erev Shabbat for that matter, Birkat Kohanim was deferred to Yom Tov when more people make an effort to immerse in a mikva before Yom Tov. (Sefer Chasidim 1613; Beit Yosef, OC 128)
See also here for other reasons.