The other day, over at Hirhurim, Rabbi Ari Enkin covered the practice of the rabbi leading the sefirat haOmer for the congregation, and what the basis for this might be. Thus:
Another reason that the rabbi leads the counting of the omer is because one who missed a day and did not count the omer is no longer permitted to recite the blessing when counting the omer on consecutive nights. As such, in order not to embarrass the one leading the services who may have missed a day in the sefira count and would be embarrassed if this information was made public, the rabbi is designated to lead the sefirat ha'omer service, as it is unlikely that he would have missed counting a day of the omer.If so, we see that this kavod habriyos makes its way into halacha, just as it does in other situations. (E.g. a baal koreh for leining, for vidui maaser, for kiddushin.)
 Rivevot Ephraim 1:334
What if the rabbi goes elsewhere during the course of sefirah, and somehow missed a day? The next day in shul, everyone looks expectantly to him to make the bracha. And he is no mere hedyot. The embarrassment of a person is in line with his stature before this. What will people say, that the rabbi missed saying sefirah?
Perhaps, from the rabbi's perspective, since he does not want to make a bracha levatalah, the appropriate and courageous thing to do is declare that he missed a day. He cannot say the bracha anyway, and so he is willing to take the hit in order to do what is right. And that is admirable.
And as Rabbi Enkin notes:
No one should be embarrassed or feel inferior for having missed counting the omer and thereby disqualified from reciting the blessing. We're all only human.But we also see that that embarrassment is not enough to allow saying a bracha, such that the first line of defense is to preempt by appointing the rabbi in the general case.
Related, is it the case that the rabbi's bracha is not covering anybody? Or does it cover someone? He writes, as another possible reason, that the rabbi, and not ignorant congregants, know the following:
It is explained that the one leading the counting of the omer is supposed to have in mind not to discharge the mitzva on behalf of the congregation in order that they be able to perform the mitzva themselves.But perhaps the reason for saying the bracha out loud is for someone who can legitimately make the bracha do so in mind for people who are uncertain whether they can make the bracha. If you miss a day, you don't say the bracha, because of a safek that we might pasken like the Behag, that the count needs to be complete, and that this is now lacking. But this is the Behag's surprising chiddush. You might indeed fulfill the mitzvah. To be on the safe side, you don't make the bracha, but still count.
So what if someone -- say the rabbi -- is placed into this situation? The same kavod haberiyot which worked to place him in this situation should work to take him out of the situation. I would not say so in general, for any bracha levatalah. But this case is different, since it is not so clear that it is a bracha levatalah. Rather, it is only within the surprising shita of the Behag, which people are choshesh for. And we don't even extend it to other cases which are akin. (See Aruch haShulchan for this.)
If so, the halacha might well be that the rabbi should make this pseudo- bracha levatalah because of this concern ofkavod habriyos.
After I wrote this, I looked back at the comment section on Hirhurim, and I saw the following:
r' vosner is mechadeish (and rav asher weiss argues) that if the rov missed a day, he can still count with a bracha. if i remember correctly, part of his rationale is kavod habriyos of the rov.This teaches me to read the comment sections. So I might be on the right track here. If someone can point me to where these sources can be found, we might have a nice followup.