The ottomans and in general all Islamic dynasties post 1200 didn’t feel restricted by this because they consciously and unconsciously operated in the traditions of government and rulership of the Iranian tradition, the Turko-Mongol tradition, and to lesser degrees the eastern Roman and Indic tradition. I’d say a reason the umayyads were limited in this way is because they weren’t able or willing to use the legitimacy offered to extra-Islamic taxes by these traditions because those traditions could justify anyone’s right to rule, as opposed to the Islamic tradition which might have seemed to favour the Umayyad dynasty.
It should be noted that the Umayyads imitated the Romans in terms of culture due to how deeply respected the Romans were by Peninsular Arabs even during Islam. One need only look at Qusayr 'Amra to find depictions of human figures with clear imitation of East Roman frescos and iconography. However it is true that the Umayyads were more decidedly Arab in their emphases than proceeding Islamic dynasties.
But it should also be noted that this Arabness was not what led them to be so constrained by Islamic law. Rather they were still operating as though they had continuity with the Rashidun and Muhammad's Caliphate. In fact, while we distinguish between the Rashidun and Umayyads in hindsight, the Umayyads themselves based their legitimacy upon being the rightful successors of Muhammad's polity. Moreover, much of the population still had memories from the era of the Rashidun.
Remember that the Umayyads lasted for only
69 years. For much of its reign, it was dealing with people and their families who knew about how the law was applied in the time of the prophet and the Qur'an which discusses taxes, from what I understand, in a negative light. Kids had grandparents who grew up in the Rashidun Caliphate. And the Umayyads were still stuck with the same institutions, structures, and laws that existed during the Rashidun Caliphate. The only difference in terms of political structure, in many respects, was who was in charge. The Abbasids and proceeding Islamic dynasties were more radically different in their political and economic structures to the Rashidun than the Umayyads were.