I am not saying
@Trotsky is necessarily wrong but I think the roots go deeper than he suggests in that first post. For instance, you point to the fall of the Ottoman Empire as a key turning point and I agree but note that both Salafism and Wahhabism emerged before the fall of the Ottomans(first Saudi state existed between 1744-1818).
The deeper root is the clash between modernity and classical Islam. Classical Islam was highly pluralistic in practice as it wasn't enforced by a powerful, centralized state with a hegemonic religious vision but rather a patchwork of courts and jurists with a variety of different views based on their
madhab and even personal approaches. You can have Hanafi, Maliki, Hanbali, and Shaifi courts all giving wildly different rulings on more or less similar cases in the same city and nobody saw anything wrong with this(in fact some people gamed the system by going to multiple different schools of jurisprudence depending on the issue they wanted resolved so that they would get favorable rulings). Why should a ruling on divorce between two Maliki Maghrebis be the same as one between two Hanafi Turks? Even within a
madhab you might find different rulings on the same kind of case as the jurist is ideally sensitive to the unique customs of different populations.
This was so because these courts were rooted in their local contexts primarily and not reliant on the state; they subsisted off of court fees and proceeds from charitable foundations they ran. Projecting modern terms onto the past has many limitations and pitfalls but in a sense they weren't actors of the state but of civil society. They attended to many of society's needs like dispute arbitration(primarily related to family issues like marriage, divorce, and inheritance), education, and charity more or less independent of the state. In fact one of their key roles was mediating the social contract between rulers and ruled, something they could do because of their moral authority and independent economic foundation. Its not that simple, some were more aristocratic and chummy with the rulers and others more populist and close to the people. But as a class that was a key function.
All that changed when the Fire Nation attacked, and by that I mean the onset of modernity. Now the state was a powerful, centralized force with a hegemonic vision for society; no longer was it acceptable for the law to be so chaotic and pluralistic, it now had to be standardized and of course enforced by the state. In practice this meant that the state took on many of the functions that the
ulema once performed making them irrelevant. And often they were co-opted, becoming agents of the state and towing the state line, thus eroding their moral authority and their ability to be mediators between rulers and ruled.
This lead to the emergence of Salafism which is paradoxically more and less plural than the classical tradition; it called for a direct interpretation based on the Qur'an and hadith without mediation through the scholarly class which means that theoretically every Salafi can have his own individualized interpretation. But unlike the classical tradition these various interpretations are often mutually exclusive. So when, for example, the Wahhabism was being spread by the Saudi-Wahhab alliance, it wasn't spread as one other acceptable vision of Islam alongside others but as the only acceptable vision of Islam. Thus the modern state allows small groups of visionaries to impose their vision on the whole of society, something that was not the norm in premodern Islam. There were exceptions like the
Safavid conversion of Iran but even then the limited capacity of the premodern state means a massive disparity in efficacy compared to any such attempts by a modern one.
So because the modern state does not tolerate the classical pluralism of premodern Islam, each group wants to race to capture the reins of the state to impose their own vision of Islam on everyone else and this is not unique to the fundamentalists. Secular dictatorships also do this to try to push a very apolitical, sanitized form of Islam on their populations as evidenced by the religious establishment in Egypt being critical of the Islamists. Everyone, from Salafists to Islamic feminists and modernists to secularists, has their own vision of Islam that they feel is the one true Islam that must be accepted by everyone else, a stark contrast to the classical tradition where more often than not rulings were seen as working conclusions that were fitted to their specific contexts and expected to exist alongside alternative but more or less equally valid conclusions.