The typical toy or oatmeal-box crystal set is very lossy which cuts both sensitivity and selectivity. The only power that an unamplified set has is the power coming in on the antenna, so for high performance, as much of that signal as possible has to be conserved. Many advanced crystal set constructors these days build sets with super low-loss tuning capacitors, air-core litz wire coils and special insulation techniques that are as sensitive as and separate stations as well as a superhet, as incredible as that may seem. Even the interchannel band flutter can be heard on some of these sets. If you search for "selective crystal set" or "crystal set contest," you'll find descriptions and pictures of such sets and see that many have logged up to hundreds of confirmed stations on their sets. Special techniques are used to keep losses low and to match sensitive headphones
to the high impedance of the set. These are unpowered sets and do not use amplification of any kind. In the case of a local flame thrower, a coil/cap wave trap can null it out.