Why is the prohibition of owning or benefiting from Hametz (leavened bread) not appear in the Haggadah?

All references in the Haggadah to Hametz are a reference to ingesting leaven and all meaning ascribed to the prohibition of eating leaven are in direct reference to the positive commandment to eat matzah ... the Jews left in haste and had no time to bake their bread.

The aspect of purging leaven from one's property and not deriving any benefit or enjoyment are nowhere mentioned. This is surprising, since as any homemaker will testify it represents the most daunting and challenging aspect of Passover preparation... and therefore, Redemption preparation.

Could it be that the purging of the leaven was left out of the Seder night by the exclusively male Rabbis who choreographed the Seder and wrote the Haggadah as a result of good old chauvinism? After all, the Magid of Mezritch was the advocate for the downtrodden, the poor, the deformed, the ignorant.  By taking the case of the women in whose hands the purge of leaven falls, and placing them at the climactic moment when deliverance is on the line, he implicity confirms that their absence, and that of the purge of leaven ... was gaping.  which brings us to the moment of deliverance...

The Seder is first and foremost about Deliverance - Geula. Deliverance from Egypt and the Final Deliverance of the Messianic Era. It is a Layl Shemurim... a night of Watching.

The four cups of wine that we drink at the Passover Seder correspond to these four phrases of deliverance in Exodus 6.  The climax comes between the 3rd cup of redemption וְגָאַלְתִּ֤י אֶתְכֶם֙ and the fourth cup of resolution. This is the moment of the Seder that corresponds to the blowing of the Shofar on Rosh Hassanah. It is here that a reference to the physical and spiritual purging of leaven necessary for the redemption would be appropriate. Instead we get a curse incantation...

Gershom Scholem in his work The Messianic Idea in Judaism points out that there have always been two aspects of Jewish Messianism.  Catastrophic and Utopian.  Think of the Day of Judgement and a day when the lion shall lay down with the lamb.  In "Pour out Your Wrath" we have only the Catastrophic.

Scholem also distinguishes between Jewish and Christian Messianism.  At the time of the writing of the Haggadah, Jewish Messianism is National and Christian is personal.

He writes: Christianity conceives of redemption as an event in the spiritual and unseen realm, an event which is reflected in the soul, in the private world of each individual, and which effects an inner transformation which need not correspond to anything outside. But it remains peculiar that this question concerning the inner aspect of the redemption should emerge so late in Judaism—though it finally does emerge with great vehemence.

In Pour Out Your Wrath we see only the external and national... if the deliverance is delayed, it is because of the Nations who know thee not...

We return to the question of why the purging of physical leaven and the leaven of our hearts is seemingly absent from our Seder. Israel Jacob Yuval details the conflagratory nature of "leaven" in Jewish-Christian tensions in the Middle Ages. In his article Passover in the Middle Ages in Passover and Easter; Origin and History to Modern Times pp 141-2 writes:

But burning leaven evoked messianic images of redemption, as we see from the thirteenth-century halakhic authority and German pietist, Eliezer of Worms: “As reward for the burning of leaven, Israel will set Esau [Rome] on fire.” Little imagination is needed to guess what Christians who observed the ceremony must have thought. On the eve of Passover, on the day which (as Jews reckoned it) Jesus was crucified, Jews removed all leaven from their home and burned it—while thinking of the destruction of Christianity and the coming of redemption. Some Jews themselves feared that interpretation....

The following event, however, reveals the danger that existed in that regard. In the year 1399, a disputation occurred between the convert from Judaism, Peter, and Rabbi Lipmann Mulhausen. The remarkable conclusion of the disputation— the execution of eighty Jews—evokes the impression that this was not a learned debate so much as it was an inquisitorial trial played out against the backdrop of the charge of host desecration [The "host" is the sacred bread used in the Eucharistic service of the Mass]. The central Christian argument was that Jews disdain Christianity and seek to destroy it: “Of all the dough that you knead, you burn a little as an affront to their God [i.e., the Christian God]. Also, on the eve of Passover, the time of the fast [Lent] you burn bread.” The accusations refer to two customs: burning challah (the ritual removal and burning of part of the dough as an equivalent to the dough offering from Temple times, before baking bread) and burning leaven. The apostate from Judaism apparently saw in both a Jewish effort to disparage the host.

Leaven in the New Testament:

Therefore let us keep the feast, not with old leaven, neither with the leaven of malice and wickedness; but with the unleavened [bread] of sincerity and truth. [Corinthians 5:8]

“the leaven of the Pharisees,” which is “hypocrisy” (Luke 12:1; d. Mark 8:15).

It could be that Leaven and the purging of Leaven had become, at least in the early days of Jewish - Christian relationships, a wedge issue.... especially given the reference to the "leaven of the Pharisees" aka followers of Rabbinic Judaism.

Another possibility is that "leaven" and the purging of leaven came to represent a personal conception of redemption which had been co-opted by Christianity and at least, temporarily, jettisoned by Judaism.

Inspired by a footnote from Israel Jacob Yuval in Two Nations in Your Womb: Perceptions of Jews and Christians in Late Antiquity and the Middle Ages p. 123 we might suggest the following piyyut (poem) which has been preserved (but not necessarily written for) the penitential service on the Eve of the New Year.