In Nasser's case, it would have made no sense, in the years before OPEC trillions (which Egypt in any case did not share in), or the millions of Muslim immigrants settled deep behind the enemy lines of Western Europe, for him, an army colonel interested in modernizing Egypt and in enlarging his own power and greatness, to appeal to any pan-Islamic sentiment. After all, his main threat were those who were completely Muslim, the Ikhwan al-muslimin or Muslim Brotherhood, founded by Tariq Ramadan's grandfather Hasan al-Banna back in 1928, when the dansants at Shepheard's Hotel were still in full swing, and the syce-runners waiting patiently outside, and Levantines were reading The Egyptian Gazette.
Nasser's only political rivals were the fanatically Muslim, and he represented not true "secularism" but rather, a less intense form of Islam. But, as he demonstrated again and again, he was prepared to use, and be used by, Islam -- and his seizing the property of, and throwing out of the country, Greeks, Jews, Armenians, Italians and others could be seen as an act of "nationalism," but could also be seen as an act against Infidels. Certainly his rhetoric before and during the Six-Day War was dripping with Islamic themes, and so was, for years, the Egyptian press. How could it be otherwise? Egypt was largely Muslim. And it is today.
As for Saddam Hussein, he realized that the Shi'a were more numerous than the Sunnis (though not quite to the extent that they have become today), and that the best way for a Sunni despotism to survive would be to disguise it as something else. Any Islam-based opposition to the rule of Saddam Hussein would have to be, among the Arabs, mosque-based. And that meant many of them would be Shi'a mosques, and that would be dangerous for the Sunni rulers of Iraq.
In Syria, Ba'athism helped to disguise the Alawite dictatorship, and since the Alawites are about 12% of the population, and with their cult of Mary are dangerously un-Islamic. In fact, one of their achievements was to receive, in recent years, a fatwa from Shi'a Muslims in Iran offering the opinion that Alawites were indeed orthodox Muslims -- but as the Sunnis might say, this may be a case of needing a second opinion. They needed such a disguise. The Alawites, a minority despised by the Sunni Arabs, came to power only as a result of their having served the French as part of the "Troupes Speciales," and then having formed a kind of military caste. Finally, the Air Force officer Hafez al-Assad put himself and other Alawites (the only people he could fully trust) in power. He could not possibly abandon "secular" Ba'athism, because he had to appeal not only to Christians (with Armenians forming one of the special household-guard units), who realized the Alawites were their only protectors against the real Muslims, but also to those Muslims who were more alarmed by the Ikhwan than they were offended by the syncretistic Alawites.
In Iraq, a similar disguise was needed by the Sunnis, which is why Iraq was the only country, other than Syria, where Ba'athism took hold. Ba'athism was the perfect disguise for Sunni despotism. It appeared to be, on the surface, a party open to all, free from sectarian or ethnic bias, so that Shi'a Arabs, Kurds, and even the odd Christian (and Tariq Aziz was very odd) might join the Ba'ath Party and to some modest degree at least claim or pretend to have a share in the power. Behind Ba'athism, however, were always the Sunni Arabs, determined to treat both Kurds and Shi'a Arabs (the Arabic-speaking Christians hardly counted, and Jews, who had in 1920 constituted one-third of the population of Baghdad, had disappeared unlamented from Iraq, having left in a hurry, harried out, sent packing, and the pogrom of 1941, or the little pogroms of 1948-1950, or the public hanging of innocent Jews as "Zionist spies" in January 1969, before a Baghdad crowd of a half-million howling with hysteria and rapturous hate, made sure that any who remained would not remain for long).
Saddam Hussein appealed to Islamic history again and again whenever he felt the need. He naturally named his battles and campaigns against Iran after famous battles in that history. He named his war against the Kurds "Al-Anfal" after a sura in the Qur'an. He built mosques, and was making plans for building the largest mosque in the world when he was so rudely interrupted by three American divisions. He commissioned Qur'ans, including one calligraphed using an ink consisting mainly of his, Saddam Hussein's, own blood. He put a Qur'anic inscription on the Iraqi flag. He spoke more and more with Qur'anic phrases and allusions to Islam. It hardly mattered how deeply he felt it; he certainly was no true secularist, but merely someone more interested in the power of the Arabs, and that power meant the power of the Sunni Arabs, and of the Sunni Arabs, it had to mean their great champion, Saddam Hussein, and whatever it took for him to retain and enlarge his power, including being open, for example, to the education of women, not because he had been reading Mary Wollstonecraft but because those educated women could learn such useful things as weapons technology (and Dr. Germ and Dr. Anthrax did), or otherwise make his Iraq, and therefore make him, more formidable.
And had Nasser lived longer, instead of dying of a broken heart from his loss in a war that he alone brought on himself in June 1967, one would not have been surprised to find that he, too, as the occasion arose, would have embraced Islam more fervently, as Saddam Hussein found himself doing in his last decade of power. First, out of political necessity, to keep the allegiance of a Muslim population. Second, because in the end, these were not true "secularists" as this word is commonly used in the West. They were simply just a bit less fanatically Muslim than some other Muslims who were their political rivals. Pan-Arabism was merely the only game in town in the early days, when independence had just come to Morocco, Tunisia, and Algeria, when Pakistan was still arranging itself, and Indonesia was under the control of the still-secular Dutch-educated local nationalists, and there was no oil wealth to support global dreams. Pan-Arabism is best seen not as an alternative to, but merely as a subset of, pan-Islamism.
And in any case, pan-Arabism and pan-Islamism overlap so much that to set them in opposition is to mislead. For in Islam it is the Arabs who, though they now constitute about one-fourth or one-fifth of the world's Muslims, continue to dominate all non-Arab Muslims. Those non-Arabs must read the Qur'an in Arabic, pray toward Arabia, take as models seventh-century Arabs, claim if they can Arab lineages, even in many cases take Arab names. Fulfillment of a pan-Arab dream would merely be a logical stepping-stone to the next goal, a pan-Islamic state, a single Caliphate with a single, undoubtedly Arab Caliph, that would use the tens of trillions still to come, and the billion unswerving believers, and the tens of millions of Believers now multiplying behind what they themselves are taught to regard as enemy lines.
Arab "secularists" do exist. Bourguiba was one. But neither Saddam Hussein, nor Nasser, were "secular" in anything like the way as the Arab Bourguiba, or the non-Arab Ataturk. Both wished to curb their political rivals, but neither was intent on systematically constraining Islam; rather, each wished to exploit Islam for his own ends. They alluded to Islamic history, appealed to their adoring mobs with Qur'anic passages, gave speeches impregnated with, or rather reflecting, attitudes naturally emanating from Islam. OPEC money, Muslim migrants in the West, and technological advances in the dissemination of Islam's message, all contributed to replace the pan-Arabism of Nasser (first self-proclaimed King of the Arabs) and Saddam Hussein (second self-proclaimed King of the Arabs, by unpopular demand) with what had once seemed merely an impossible dream: pan-Islamism.