For what it's worth, until 1991 (my first year of college) I had never been in a shul where Birkat Kohanim occurred at any point--and these were all shuls that DID give Kohen & Levi aliyot, not rishon & sheni.
At the student-led egalitarian Conservative high holiday services my roommate and I went to, she was apparently the only person (male or female) whose father was a kohen and so could perform Birkat Kohanim. Her parents had not been observant Jews and had raised her without much of a religious upbringing, but she had become far more interested in traditional Judaism and had in fact been keeping kosher since 10th grade (telling her parents she was becoming vegetarian, since bad blood between them & an Orthodox relative made her reluctant to thrust her new observance in their faces). In this case, the tradition of having the person pronouncing the blessing be "fed" it word by word had exactly the desired effect: having never performed this ritual before -- indeed, probably never having seen it performed before either -- she was able to convey this blessing to all of us, without concern about whether she would remember all of the words. It was a wonderful moment.
Since then, I can count on one hand the number of times I've seen birkat kohanim done in any shul of any sort*, but in many of those places it had been added to the practices of the shul or minyan relatively recently, having either never been done or not done within memory of anyone there.
Me, I can take it or leave it -- as with kohen-levi aliyot vs. rishon-sheni -- as long as all those whose fathers are kohanim or levi'im (i.e., including b'not kohen/levi) have these ritual roles/honors extended to them regardless of gender.
But I concur in the understanding that several have voiced here that birkat kohanim, which is extended through but not on behalf of the kohanim, need not be anathema in a shul that dispenses with kohen/levi aliyot -- as well as in thinking that other ways of conveying this blessing may also be valuable in making the members of the congregation feel the impact of receiving this blessing in some way that is more striking or immediate than its recitation by the shaliach as part of ordinary Amidah repetition.
* Those occasions were:
- Rosh Hashanah at an egalitarian Conservative syagogue in Albany, NY (done by both women and men whose fathers are kohanim);
- a Sukkot service of traditional egalitarian Conservative minyan members in a friend's backyard in Washington DC (both men and women whose fathers are kohanim -- though I heard some grumbling/challenging from some traditionalist men re: having a bat kohen up there);
- high holiday services at a Conservative synagogue in Maryland (egalitarian shul, though only men were up there; according to one authority I asked afterwards, b'not kohen are also allowed to do so -- but I heard from others that at some point in the past a bat kohen had done so & then been given some grief about it);
- chag services at Young Israel in Manhattan (Orthodox, not egalitarian, so only men);
- Pesach services at a Chabah shul in Cleveland (ditto).