Well, its elastic modulus and yield strength are pretty important, actually. Being stiff and strong is pretty fundamental to a lot of its uses. It's stiffer and stronger than most other everyday materials and virtually all everyday
plastic materials. Glass, quartz, alumina, zirconia, and porcelain are stiffer than steel, and glass can be stronger, but they're all brittle rather than plastic, which is pretty inconvenient and often makes them very weak in tension. Wood, most other fired clay, aluminum, brass, nearly all organic polymers, mica, cotton, dirt, etc., are much floppier and weaker than steel.
But there are a lot of metals that are somewhat stiffer and stronger than steel, like chromium, platinum, and tungsten, while still being somewhat plastic. The great advantage that steel has over them is that it's unbelievably cheap. It's even cheaper than brass, bronze, and lead!
Plasticity (ductility and malleability) is important for a couple of reasons. First, as I mentioned above, it greatly increases the fraction of the material's theoretical strength you can get in practice. Second, it allows you to form the material instead of cutting it to shape. That's the property you're using when you wrap a sandwich in aluminum foil or tie a gate shut with baling wire. You can't do that with porcelain foil or porcelain rod. Third, ductile failure happens gradually rather than suddenly, which is important in some cases.
The other really interesting thing about steel is that it's hardenable. This is very significant because cutting and forming hard things is hard. So it's routine to cut or form steel in its soft state to get more or less the shape you want, harden it, and then grind it and maybe lap it to the precise shape you want. Grinding and especially lapping can be very precise and cut very hard materials, but they're very slow processes.
Finally, steel can withstand much higher temperatures than organic materials, or even most other common metals.
These are, I think, the major reason why steel has so extensively displaced what Andrew Carnegie liked to call "inferior materials".