OK, a confession: it is a long time since I last listened with a shortwave crystal set.
One thing is certain: at the right time it is possible to hear true worldwide DX, and not via relays.
These days there are fewer English language SW broadcasters and it is much tougher. We are also in a period of declining solar activity, so fewer HF bands are open and these stay open for less time. Nonetheless, crystal sets are easy to make and require no power. DXing with crystal sets is a fun activity.
One of my many planned projects is a multi-band crystal set capable of covering from VLF to VHF. It may never get made, but this would be fun.
See https://sites.google.com/site/g3xbmqrp3/hf/crystalset .