That's a very good question by Bob.
The jpg you send to whatever company prints the photo ("I order hundreds of photos") has the date in its metadata.
If the website where you order the prints should have a few checkboxes where you can choose what of those metadata you wanted to see on the print, they would do the job.
A useful piece of metadata (apart from date and time) for some might be the GPS-coordinates, so you can see on the print where the photo has been taken. This could easily be translated to, for example, the name of a city or even a street inside it.
It's much easier for the printing company to do this than for the individual that places the order.
Here's a business opportunity!