No reason to stay away from them, as you can turn this "feature" on and off in the camera's menu. So all you need to do is familiarize yourself with the menu.

The Canon D11 has that feature, as that is the camera this thread was started with.
My E-5 has that feature, I always make sure it is turned off.
My E-M1 does not, so no worry.
My C-4000 showed time and date while playing back, and could be printed on the photos as well.
Our old film Ricoh camera also could print the date on photos.

But what program does that?

I have owned cameras in the past that will superimpose the date stamp on the photo and when it's on it takes careful editing to "get rid of it" - it is a "feature" that needs to be turned on or off in the camera's menu.
Even as far back as film cameras, and often wished the camera would put the date in the film's margin, NOT on the photo itself. Because of that, I always turned it off.

Over the years, I have also tried out a large number of editing programs, and have never run into one that takes the date from the exif and superimposes it on the image.

With all due respect, BigBear, I believe that you are mistaken: the date/time stamp that shows up on photos in bright orange letters is placed there by the camera. To my knowledge there is no program that will superimpose dates or any other information onto a photo - at least not without the user's input.