This was not always the case. In 1912 Pathé released two reels (perhaps with the intention of distributors showing them together) Agar e Ismaël and Le Sacrifice d'Ismaël by Henri Andréani. Both films featured Ishmael in the title, even if the short running lengths prevented any complex characterisation.
Perhaps the most intriguing portrayal was in Huston's 1966 film The Bible. Ishmael, still a boy, desecrates a sacred ceremony marking Isaac's weaning. Sarah is appalled watching Ishmael snatch, toss, smash and bury the ceremonial doll, which is, presumably, Isaac's effigy. Sarah views this as a portent of the boys' future relationship, and Ishmael's desire to forcibly assert his authority over his younger brother. To the viewer this appears as simply childish play in an inappropriate context; the result of over exuberance, or perhaps bad parenting. Abraham, however, seems unsure not only torn by his love of his son and the complaints of his wife, he is perhaps as concerned by Ishmael's willingness to stray outside of the accepted religious ceremonial norms. God's voice-over assures him that he need not worry about Ishmael's fate, but also raises the question as to whether Ishmael would have been quite such a willing participant in Abraham's later "test of faith".
One consistent feature about the Isaac episodes is the negative portrayal of Sarai/Sarah. Whilst some of this is derived from the text itself, few films seek to understand Sarah, let along sympathise with her. Indeed most films depict her in an even poorer light than the texts, showing her treating Hagar harshly, (for example carrying heavy loads even when very heavily pregnant). The portrayal of Hagar is often similarly unsympathetic. Whereas the text says only that she "despised" Sarai, several films show her criticising Sarai to her face for being barren. The intention here consistently seems to be to portray Abraham as decent, sympathetic and essentially good. Unfortunately given that he would have been her social superior. He comes across as weak and controlled by Sarah, rather than the master of his own destiny. The consistently shrewish portrayals of Sarah are bolstered by many films using a voice-over to inform the audience that God has also reassured Abraham that he is making the correct decision.
The efforts to beatify Abraham also extend to the portrayal of Ishmael's conception. Almost universally this is depicted as Sarah's suggestion. Indeed the only film to show any flicker of interest from Abraham at the prospect of having sex with Hagar is the irreverent comedy The Real Old Testament (2003) where he feebly tries to shroud his glee at the very prospect. The 2013 miniseries The Bible sexualises Hagar still further by not only choosing an actress with "model looks", but also dwelling on her naked back as she lingers in the tent after conception, watching Abraham walk away unmoved by what has happened.
At this point in the biblical story, Hagar runs away, meets an angel/God in the desert and returns with prophetic words about his future ringing in her ears (Gen 16:6b-14). The similarities between this (Yahwist) account and that in Gen 21:14-19 (Elohist) have meant that the majority of films featuring Ishmael have only included one or the other, sometimes harmonising the two. The one exception is Abraham (1994), the longest portrayal of the Abraham story.
Ishmael's early days are captured in a variety of ways, in some films Sarai takes to the new addition to the family, whereas in other there is enmity from the start. Yet it's perhaps the 1994 film that is most interesting here as Sarai and Abram coo and delight in their son while a still recovering Hagar has to watch from a distance.
Such nuance is however generally absent from the later scenes featuring Ishmael, indeed it is only the Abraham entry in the Testament: The Bible in Animation series where he is given a proper line. There are a few hints of his prowess with the bow (Gen 21:20) in Abraham (1994) and The Bible (2013), but, aside from the incident in the Huston film, Ishmael only needs exist for Sarah's anger to be kindled.To that end it's perhaps not surprising that only one film, In the Beginning, (2000) shows Ishmael's appearance at his father's death bed (pictured above). It is clear from his arrival at the head of a group of horsemen that the angel's words about his prosperity are already coming to pass.