I have read somewhere (I will try to find where) that there is a risk of structural damage (in the wing tanks) if you feed the engines by gravity unless sufficient time passes after leveling off at cruising altitude.
I think it has to do with the venting of the tanks. The pressure of the air in the tanks is not the same as the atmospheric pressure when the airplane is climbing. Apparently it takes time to be the same. Although I don't quite understand it very well, to be honest. Why does not the same problem occur with the pumps running?
We need an engineer for this one.