I think saying that early Muslims did not encourage conversion to Islam for financial reasons is a far too simplified way of viewing the Arab Conquests. The Arabs were interested in spreading their new religion, especially through conquest as we cannot disentangle Islam from its military successes. Recent studies, particularly those by Robert Hoyland, James Howard-Johnston and Fred Donner, have emphasised the role of faith in pushing the Arab armies onwards. Looking at Professor Holes' profile here, I get the impression that he is primarily a linguist and so not a historian of early Islam, so this might explain why he did not take into account recent scholarship in this area (even though both Hoyland and Howard-Johnston are at Oxford as well).

It is true that the Arabs did not actively force local Christians, Jews and Zoroastrians to convert, but there were plenty of other reasons as well in addition to simple financial logic. Early Islam was a movement that explicitly included adherents of other Abrahamic religions, with Christians and Jews taking an active part in the conquests (many Arabs living in Syria, Iraq and the Arabian borderlands were for example already Christian by the sixth century). There really was no religious reason for them to forcibly convert these people when early Islam was a large umbrella movement that fully accepted them - pagans were the target, not them. This was I think the case for Egypt, Syria and Iraq, where Christians have long been the majority. Of course political and financial expediency were important, but so was their faith.

As for why the Arab Conquests happened, I can only give you a brief overview for now, as it is a hugely complicated (and controversial) topic. For me, religion did play a major role. The seventh century was a time of plagues, mass warfare and religious persecutions, so throughout the late antique world there was a sense of an impending apocalypse. The Qur'an seems to be a product of the same milieu and Muhammad was probably preaching against pagans and urging others to live godly lives in preparation for the end of the world. By extension, this also implied the conquest of Jerusalem, a key part of their Abrahamic inheritance. Then there are the material factors. The Romans and Persians had exhausted themselves after fighting for over two decades, so the rich provinces in the Near East were ripe for the taking for those willing to fight for it. In all honesty, it was probably a mixture of both religious and material reasons that led to the Arab Conquests, to think otherwise would be ignoring how complicated humans were (and are).

This might sound surprising, but the reason I can't give you a definitive answer is because of how unsettled the field of early Islamic history is right now. Since the 70s, the trend in academia is to re-examine the sources critically, with the result that we are far less confident of the narrative than we were before. Take Muhammad's death for example. There is actually no good reason for us to think that with his death Arabian raids escalated, as raids were common throughout late antiquity and had been escalating since 602 when the Persians and the Romans began their last destructive war. Nor is it proven that the death of Muhammad happened before the armies of conquest (see here for some extracts from primary sources implying that Muhammad had a role in the conquest of Palestine). A more plausible answer is that many Arabs, both those in and those who were not in Muhammad's confederation, had engaged in raiding activity around that time. Over time, Muhammad's confederation became a dominant one and gradually transformed themselves into conquerors from the 620s onwards.

For more detailed answer about why the Arab Conquests succeeded, especially from a Roman perspective, check out my comment here. Let me know also if you have any other questions about this, as I definitely did not cover everything!

"for the purpose of spreading Islam" They certainly wanted to increase the area under the political control of Muslims, and paying taxes to Muslims, but conversion wasn't the primary goal for the reasons you cited. In the beginning, simply professing "There is no God but God and Muhammad is his messenger" wasn't enough for conversion, you also had to have a Muslim Arab adopt you into his tribe.

Under Abu Bakr, the first leader after Muhammad, the first raids north were raids, not a planned invasion. After several victories against the Byzantines and Persians, the Muslims kept pushing outward, capturing cities and taking territory. They believed that God had given them the final truth, their victories were proof of the rightness of their cause, and conquest made them rich.

The counterbalance to the picture of the early Muslims as looters rampaging across the known world is the lack of a destruction layer [1] in most cities at the time and accounts of heterodox Christian minorities welcoming the Muslims (lower taxes than the old empire, and less concern for their doctrines). The Muslim rulers also set out to segregate their armies from the people they had conquered by creating garrison towns or amsar (sing. misr). This was meant to keep the "purity" of the Muslim army intact, and stop them from getting soft.

[1] There's a lot less archaeological data on this time period than you'd hope. This statement comes from Fred Donner's Muhammad and the Believers other sources: Marshall G.S. Hodgson: The Venture of Islam Vol 1 Barnaby Rogerson: The Heirs of the Prophet Muhammad