There is a well-known macroeconomic response to this question. Since GCC national currencies are fixed to the US dollar (except Kuwait?) and therefore monetary policies are unable to effectively deal with rising and persistent inflation; as a result only the real economy adjusts in terms of higher prices.
There are also two less-known microeconomic reasons that seem to answer the current inflation episode in GCC quite well. First, there is a widespread incentive problem. Still today (and for several years to come) GCC governments do not need to rely on tax revenues to finance their expenditures. Naturally these governments have little incentive to protect public interests. There is also a reverse causality. The citizens have little or no incentive to push their governments to fight inflation, not because of the constitutional monarchy, but because of how easily they buy social peace (e.g. cheap housing and medical care, free education, generous child subsidy, easy employment opportunities, and many more). May be the Gulf citizens deserve these benefits as part of their oil share, but surely these generous benefits have helped to downplay their concern over inflation.
Second, disutility from exerting (additional) efforts. More monetary flexibility to fight inflation involves collecting timely data, conducting more research, and importantly reading more literature. Thus far the Federal Reserve has been doing all these work for Gulf central banks; depegging from the dollar means shift of the academic burden from the West to Middle East. Of course, GCC states could hire (and is hiring) additional skilled workers to do most of the work, but at the end timely monetary policy implementation would also require greater commitment from the native decision-makers. Certainly GCC central banks are not used to serious work and making the commitment to embrace flexible monetary policy is more of a disutility from work rather than a necessary step to curb inflation.
The Economist once said it right: as the Indians and Chinese work harder, the Gulf gets richer. The windfall oil revenue has brought a honeymoon effect for the region and it is against human nature to think about serious stuffs during the honeymoon period.