"You're not taking into account the moduli of the materials, which really makes a large difference in a calculation such as this, if I'm thinking about it correctly."
titanium has a higher modulus than aluminum, so given the same size beam, an aluminum one will bend more than a titanium one under the same load
however, aluminum is lighter than titanium. so, in theory your beam can be made of thicker aluminum. this added thickness will make it bend less under the load and it will be on par with the titanium beam from the first example.
so you have a modulus vs. density comparison for some given beam shape. funny enough, steel, titanium, aluminum, and magnesium are all kind of equal to one another in that comparison.
the trick to the above scenario comes down to volume. a magnesium beam that supports a given weight while only bending a certain amount is significantly larger than a steel beam that weighs the same and bends the same under the load.
here is where carbon fiber is a winner. it has a high modulus and a low density compared to those metals.
of course we are talking about tent stakes here where modulus isn't really important due to the application. the stakes are being axially loaded when driven in. strength of the material will be more critical. strength can be increased for a given material by certain treatments and alloys. 7075 is very strong aluminum. still bends as easily as the other aluminums out there but it takes more force to deform it permanently. titanium is even stronger than that. titanium is harder too so given the same shape the titanium will hold it's point better.
but here come the old weight thing again. more aluminum could be used to change the shape to make it more resistive to deforming
now I'm just babbling on… but usually innmy line of work it comes down to more than just a couple parameters to determine the optimal material for a given application
one thing that titanium has over other materials is that it is very resistive to corrosion and it maintains it's strength better at higher temperatures. neither of these usually comes into play in the backpacking community soni kind of think of it as a gimmicky marketing material in most outdoor sport applications