Actually, a better question is:
Why not an RC or LR filter?
The RC filter drops DC, which is bad. Or, if you omit an explicit R at all, the Rds(on) of the switches comes into play, which is even worse. If Fsw << 1 / (Rds(on) * C), the switches have to charge and discharge the C fully, on each switching transition -- and probably, smoke shortly follows! And, needless to say, no actual filtering is accomplished, you still get a square wave output. If Fsw is much greater instead, then the output ripple voltage might be low enough to be useful, but the transistor(s) are burning up in just a few cycles now, dissipating orders of magnitude more power than a basic linear regulator would.
So, RC sucks. Scratch that.
But what about LR? That's totally a thing.
In fact, you can think of the LC filter as an LR filter, with extra C bypass to help it along. The L works, because the transistor(s) are happy switching into a load that doesn't draw huge current spikes. The load is happy...ier, because it's not seeing a raw square wave, compared to the RC case. But a pure resistive load sees ripple voltage = ripple current * R, which is probably still a lot. To get a smooth output, you need quite a lot of L, to get the ripple down. But that's expensive.
For loads where ripple voltage doesn't matter, this can be advantageous -- high power LED drivers, for example. Here's one:
http://seventransistorlabs.com/Images/LED_Light2.pngThe FJPF13009 is the switching part of the buck converter, and the UF5404 is the flyback diode. The series 1.8mH choke feeds a bunch of LEDs, with a current sense resistor at the bottom. As long as current doesn't drop to zero, the LEDs stay fully lit. (The light intensity will always flicker at the switching frequency anyway, whether current drops to zero or not, so this doesn't even matter, really. As long as it's fast enough not to see, it's not a problem.)
Why not do this for most circuits? Because most circuits are more sensitive to ripple voltage, and most circuits require a low impedance at high frequencies -- bypass caps. Because the cap soaks up the extra ripple current, you can use a smaller and cheaper inductor, too.
Tim