1. Daylight backlit (you not subject) LCD can be very hard to see or be critical judging.
2. MUCH more battery drain vs LCD only being active for review purposes.
.... Yeah that a third thing, in low light, arms length holding it out vs braced against your body is FAR less stable.
This sums it up for me, plus a couple more things....
4. I find it impossible to capture a good panning shot of a fast moving object with an LCD and extended arms. However, using the viewfinder like a rifle scope, its a piece of cake.
5. At concerts, they usually prohibit you from taking photos. In the darkness of the audience, a bright LCD will give you away in second, a viewfinder does not. (also see point 3 to minimize image blur in concerts).