It would really depend on this culture and personal style. Histories, Jewish and Greek, might typically contain first person opinions or editorialising, but the depiction of facts, even if eyewitnessed, would necessarily be so. Part of the style of the era.
Luke writes in the first person in a couple of places in Acts, presumably to indicate that he was travelling with the people when events occured, and at the very beginning of Luke. Mark is generally held to be largely based on Peter's story, while Matthew writes for a Jewish audience and his style is particularly different from the other synoptics. The most likely candidate for direct eyewitness authorship is John, but given the particularly theological contour of his book, and the fact that in all likelihood he wrote it in the twilight of his life, we shouldn't expect him to be writing in first person either.
But really, the most concise response is this - the most vivid and ever present examples of eyewitness testimony today are in newspaper articles. Journalists quote people who give eyewitnesses testimony, but aren't necessarily eyewitnesses themselves. This does not, however, change the fact that their articles constitute eyewitness testimony.