I note that you say can be, but even so that’s surely too much of a generalisation. There are examples of Orthodox Churches that aren’t too tied to the state and also examples of non-Orthodox Churches that are.
Prime offenders, of course, would include Russia and Serbia. On the other hand, none of the Churches directly under the Ecumenical Patriarchate have any ties to their respective states, save the restrictions placed upon the Patriarchate itself by Turkey’s at any rate notionally secular government. Likewise the Churches in the Levant and north Africa. In Greece, Church and state are mutually committed to a process of separation and secularisation.
It would be hard to deny, on the other hand, that in Ireland the Catholic Church was too tied to the state. For more than thirty years Archbishop McQuaid was a ruler in all but name. Ultimately, this did the Church no favours, as recent history has shown, as decades of corruption and malfeasance were uncovered and as people came to resent the Church’s intrusion into spheres of life that were beyond its proper remit. One could also point to the close relationship between Church and state in Franco’s Spain and Salazar’s Portugal.
The UK is a very different example, but a good one nonetheless. Our head of state is also Supreme Governor of the established Church of England, and it is a legal requirement that only a member of that Church can succeed to the throne. 26 Anglican bishops sit in the upper house of legislature with the same right to speak and vote in Parliament as our elected MPs and the appointed and elected peers (the three most senior bishops are also members of the Privy Council). Neither house of Parliament can sit until prayers have been read by an Anglican cleric (a priest in the Commons, a bishop in the Lords). Diocesan bishops are appointed by the Queen on the advice of her prime minister and no bishop can be consecrated without the Queen’s mandate. The Queen also appoints many cathedral deans and even some cathedral canons. All clergy are required to swear an oath of allegiance to the monarch, and the monarch’s coat of arms is displayed in all churches. Furthermore, the Church of England’s General Synod is subordinate to Parliament, which must approve all synodal legislation, and the Church’s canon law is an actual part of the laws of England, enforceable in courts that are actual courts of law. That situation is perhaps more benign, but certainly more extreme, than those pertaining in any Orthodox country.
While Orthodox Churches certainly can develop a harmful relationship with the state, partly as a result of the national and autocephalous nature of many Orthodox Churches, it is, unfortunately, a problem that can also arise with Catholic and Protestant Churches as well.