Why do we destroy t'rumah and challah instead of giving it to a kohein?
I was thinking about t'rumah, which historically was designated for a kohein but today we destroy, and similarly taking challah, which we burn. Why isn't this a violation of bal tashchit, do not waste?
If you're an active part of a Jewish community you know how to find a kohein -- one always gets called to the torah, and they're all called up for birkat kohanim. (Let's set aside cases where a community has no kohanim.) And for a different matter involving kohanim, specifically redemption of firstborn sons (or donkeys), we find an actual kohein rather than setting aside the coins to be destroyed. Why can't we do this for food, too? Some kohanim would surely appreciate getting challah deliveries on Fridays.
Maybe the t'rumah case is unavoidable because (I think?) the kohein is required to eat it while ritually pure and none of us are today. But I don't think that applies to challah, does it? Kohanim certainly eat from the communal challah at kiddush, along with the rest of us.
What am I missing?