Dubbing is expensive; subbing is much cheaper to do. Anime translation companies usually want to dub because they have no shot at getting it aired on TV outside of Japan if there is no dub, so they usually sell the subbed DVDs etc. for about the same amount of money as the dubbed ones, in order for the sales of the subs to to offset the larger cost of dubbing. Neither dubbing nor subbing requires editing/adding to the artwork (dubs are an audio track; subs are a separate text file that can be overlaid over the art).
In contrast, usually text messages and other text shown in the artwork itself often moves as the "camera" pans; it is not usually static and flat on the screen. Covering it up would require the company to overlay art that moves: essentially, to animate over the Japanese text with text that can move along with the "camera" panning motion, to avoid scrolling the overlay over the character's fingers, to tilt at the same angle as the cell phone screen is being held at, etc. In other words, it is a different endeavor than either recording audio or typing up subtitles: one that requires more work which is a different type of work.
If the company has managed to land the series airing on TV in the country they're licensed for release in, the amount of money they expect to make off of it would cause them to be willing to re-animate those text messages. They would not have a large motivation to add that animating work on top of their dubbing expenses if they do not expect to make a lot of money from the series. If the text message is read aloud in either the voice of the sender or the voice of the recipient, it does not require the re-animating work for the viewer to understand (assuming the dub script is accurate, which is a whole different can of worms). Using the dub voice actor they've already hired to orally take care of the viewer getting the gist of the message saves money.
An alternative would be to add a subtitle track which subtitles only the on-screen text messages, book covers, signage, etc. which would be inexpensive to do. However, when you compare the dub script with the subtitle script from the same company, there are often differences because the dub is 1) attempting to match animated mouth movements and 2) attempting to sound more colloquial (i.e., "What would this character say if this character were talking naturally in English/Chinese/whatever language is being dubbed?" rather than repeating awkwardly in said language a translated phrase that a Japanese person would say in this situation but which a native speaker of said language would never think to say in this situation) as compared to the sub which is more concerned with 1) fitting in the physical space of 1~2 lines of text on the screen at once and 2) just translating more simply (what the character said). So when the dub and sub scripts do not match, it would cause more confusion to add that sub script they already made into the dub copy, because then the dub actor's voice reading the Japanese text message and the sub at the bottom of the screen would not match. It is likely that the company doesn't want to make a separate subtitle file for the dub copy unless it is necessary, again to save on costs.