Why do the photos taken on my HTC One X not have a date/time displayed on them? When I take a photo on my HTC One X, the date and time that the picture was taken do not appear appear (printed) on the photo. I can't set the date or time in the settings, either. If I use a third party application, I can set the date/time and see the timestamp on the photo.

My old HTC Legend (Gingerbread) had an option to choose whether the timestamp would appear or not.

Is it a feature not supported by Android 4.x, or is it just because of HTC One X model? It was not present on Ice Cream Sandwich or since I've upgraded to Jelly Bean.
This feature is rather be app-specific. Probably the default photo app on your Legend does this by default, while the one on you One X does not. To achieve the desired results on your new device, you might need to find a 3rd party photo app supporting this feature. Your phone is certainly capable of it, that's not the issue.