The archival argument
Proprietary RAW formats are documented by nobody and supported at the manufacturer's discretion. Cameras are discontinued, companies leave the business, and software drops support for bodies nobody uses any more. A CRW file from 2002 is already awkward to open with current tools; there is no guarantee your current camera's format will fare better in twenty years.
DNG's specification is published, which means anyone can write a reader without reverse engineering, and the format is stable across camera generations. For anyone maintaining a long-term archive, that is the entire case: converting to DNG trades a small amount of convenience now for a much better chance of readability later.
What converting actually does
Adobe's DNG Converter reads a proprietary RAW and rewrites the sensor data, unchanged, into the DNG container along with the metadata. No image data is lost. Files typically shrink by 10–20% thanks to better compression, and you can optionally embed the original RAW inside the DNG — which removes all risk at the cost of a larger file.
What does not survive is manufacturer-specific extras: in-camera Picture Controls, Active D-Lighting settings, proprietary lens correction data, and other vendor metadata that only the maker's own software reads. If you rely on Canon's DPP or Nikon's NX Studio to reproduce the camera's rendering, converting to DNG will lose that.
Native DNG and linear DNG
Several manufacturers skip proprietary formats entirely and shoot DNG directly — Leica, Pentax, Ricoh, and Hasselblad among cameras, plus DJI drones and a large number of phone cameras when shooting RAW. For those, DNG is simply the native format with no conversion involved.
There is also a variant called linear DNG, in which the demosaicing has already been done so each pixel holds full RGB values. It is produced by some processing pipelines and by cameras with non-Bayer sensors. Files are considerably larger and some of the editing latitude of true RAW is gone, though the extra bit depth remains.
The case against converting
It is a real workflow cost: an extra step on import, time spent processing, and the loss of vendor-specific metadata. Some photographers keep both, which doubles storage. And in practice, mainstream editors have kept support for old formats going for a long time, so the doomsday scenario has not yet arrived.
The honest summary is that DNG is clearly better for long-term archival and clearly worse for day-to-day convenience. Which matters more depends on whether you expect to care about these files in twenty years.