Academically, I believe you are correct in that you could potentially optimize an I-beam to have a higher failure-load to mass ratio. You would have to play with the area moment of inertia equations to check for sure. T-beams would be the extreme of what you are proposing. They are less common, but composite steel/concrete T-beams are used extensively in parking garages, with additional steel in the lower tensile section.
It is important to note that many structures are design-limited by maximum deflection rather than structural failure. Additional area on the tensile member will reduce this defection. It would be interesting to see how deflections would compare between a symmetrical and the hypothetical failure-load optimized beam.
Symmetrical is superior for torsional loads or compound loads where the flange loading may be variable. Symmetrical is also superior for columns because it reduces eccentricity and the potential for buckling for a given mass/length.
Being able to use a beam in multiple situations is important because structural steel is a commodity. The price of a particular style of I-Beam is inversely proportional to how much it is used in industry in your region. This is often a bigger factor than the cost of the additional steel in the beam or cost of the additional mass in your design.
Additionally if your structure requires lots of trapezoidal shapes, you want to use symmetrical material so you waste less material.
Right-side-up > Upside-down > Right-side-up > Upside-down...
Also, for every symmetrical beam, it saves the engineers an orientation specification in the drawings, and saves the fabricators a potential error.
Here is a good I-beam thesis to research further.