A common criticism from those who are unwilling to consider the possibility of reincarnation is that "Everyone always thinks they were Cleopatra or Attila the Hun". Actually, nothing is further from the truth. The overwhelming majority of past life regressions show very ordinary lives, often as foot soldiers, servants, small farmers, slaves or peasants. If you think about it, this is to be expected - most lives lived today are those of ordinary people, even with our modern culture of 'celebrity'. In the past the proportion of famous to plain would have been even smaller.
Ordinary lives can provide huge learning experiences. It is not necessary to be be a famous person (today any more than in yesteryear) to experience all of life's emotions. In fact, some of the hardest, and most valuable, lessons have been learned in very humble bodies.
It is of course possible that reincarnations of well known characters are walking the earth at this time. The famous reincarnate as much as anyone else. In terms of a soul's learning, a life as a king, bishop or film star is no more useful than one as an ordinary 'Joe Soap'. What is 'better than' when in the body is definitely 'the same as' to the soul.
It is also possible that a person may see themselves in a famous life, not because they were that character, but because something about the character resonates with the modern person's present life. For example, a woman who feels betrayed could see herself as Anne Boleyn. This is not because that person actually was Anne Boleyn, but because the story can clarify to her that she feels as hard done by as Anne must have felt.
The other explanation is that the modern person may have had a past life in the entourage of the famous.
Having said all that, I have never regressed anyone into a 'famous life', nor have the dozen past lives I have experienced been of any historical note. But more of them another time!