This was a big feature on some film cameras but has made little headway on digital cameras.
Even on film cameras, most would only print date or time, not both. There may have been some that did both.
Digital cameras include date and time within each picture file and it is called EXIF information. The EXIF also includes such info as camera, f-stop, shutter speed, focal length, etc. The camera makers probably feel that is sufficient.
As you stated some digital cameras will print the date on the photos, I have not seen one that will print the time. I have used the Konica Minolta Z2 and it can print the Date - but not the time.
Few digital cameras can print the date.
The ability to print dates is never included in the specifications. You have to dig through the owners manuals to find it.
Maybe someone on this forum will know of a particular camera that can print date and time.
I'm looking for a point and shoot digital camera that has both the time and the full date stamp feature. I've seen some cameras that have either one but not both. I've searched in the specs pages, but none list this feature. At this time, price is not a concern.
Appreciate any help.