A lot of the art of radio design is in rejecting as much of what you don't need as early as possible.
Consider that a wideband antenna feeding a LNA will expose that amplifier to many signal that you are not interested in, possibly causing the amplifier to become non linear and causing distortion to the wanted signal (Or even burying it in intermod to the point that you cannot even detect it). This is why a LNA at the antenna should generally only have sufficient gain to amke up cable losses, and even that can be problematic.
Sure you can place a filter ahead of the amplifier, but then the filters insertion loss directly impacts the overall system noise figure.
Considerations like this apply right down the chain, you start off with as narrowband a signal as the antenna can be designed for, use a tuned amplifier, filter it some ahead of the first mixer, filter it some more at the IF, do some more in the DSP.... At every point overload becomes less of a problem, as the bandwidth narrows in on what you care about.
73 Dan.