Let's note some properties of steel and titanium. For steel, we choose 4340 alloy (oil-quenched and tempered); for titanium, we use the Ti-6Al-4V alloy (solution heat-treated and aged). These are not the 'default treatments' for either material, but put them both in a good light. Note that for titanium, the difference between low-grade and high-grade is not quite as significant as it is for steel.
| Steel Titanium
------------------------------------------
Density: | 7.85 4.43 g/cm3
E-modulus: | 200 119 GPa
Yield strength: | 1520 1103 Mpa
Thermal expansion: | 12.3 8.6 10^-6 K^-1
Thermal conductivity | 44.5 6.7 W/mK
Cost | 3.60+ 66-154 USD/kg
Data taken from Callister & Rethwisch, "Material Science and Engineering", 2011, and matweb.
First, it is immediately clear why one would consider replacing titanium; it's mindbogglingly expensive. But is the alternative any good?
Let's look at what stresses heating could induce. We consider for simplicity a uniform rod clamped at both ends, heated up by a temperature difference $\Delta T$. The stress resulting from this temperature differential $\sigma = E\alpha_l\Delta T$ with $\alpha_l$ the thermal expansion coefficient. We rewrite for maximum allowable $\Delta T$ by equating $\sigma$ to the yield strength, $\sigma_y$.
$$\Delta T_{max}=\max{\dfrac{\sigma_y}{E\alpha_l}}$$
Thanks to the low thermal expansion, Titanium is a clear winner here, with almost twice the maximum allowable temperature difference, at 1078 kelvin difference versus 618. Note however that steel does have a significantly higher thermal conductivity, so it may be able to transport heat away more efficiently (at the cost of things becoming hot where you don't want this...).
Of course, for various other parts, different guidelines exist; in simple tension loading, we could want to maximize ${\sigma_y}/{\rho}$ with $\rho$ the density (titanium is ~25% better than steel); in compression we could want ${\sqrt{E}}/{\rho}$ if we consider buckling (titanium ~35% better than steel). The key point here however is that none of them make a good match towards titanium, especially if we consider steel that is simply annealed or rolled rather than having special treatments. This is mostly due to its low density. Since making a plane fly at Mach 3 is quite an engineering challenge, the price-tag of the materials may be a lesser issue, and just making a feasible design given any material is quite the challenge.
The bottom line however is that everything is impossible until someone makes it, but until there is a very good incentive to make a supersonic aircraft from steel, it's not going to happen.