Is there a compelling reason to use use or not use fireplace ashes in my
compost pile?

I doubt I'd ever put them in my compost pile, but I spread them about the
beds of my lilacs. They absolutely love it -- seems like they grow higher
and higher ever time I cook out.

An important item to note -- if we're talking about normal wood, i.e. the
kind you collect in the forest and such, then you should be fine. If you're
talking about processed stuff (like you would buy in a lumber yard for
example) then you may wish to reconsider. If the wood has been treated in
any way then definitely do NOT burn it. Same goes for woods like poison ivy
and the like -- gives off noxious fumes (toxic in some cases).

We typically burn maple, walnut, and occasionally a few other junk trees in
the yard that lose branches. We'll be burning even more if I ever get that
firepit dug in.

James