It’s a matter of using the most suitable material for the job.

Wood glue is meant for tight, flush joints and excels in this role as it’s thin enough to spread evenly, fill tiny cracks and dries either clear or very slightly yellow. Basically, it’s tidy.

Construction adhesive is meant for much rougher connections where surfaces that aren’t as smooth or flush and you’re probably only applying spots of adhesive rather than covering the whole surface. As such, the stuff is much thicker, more gloppy and you basically only want to apply it where it’s never going to be seen or touched because it’s messy, impossible to fine tune and looks like crap.