+1 to Paul Johnson's warnings about the challenges of diversification (how many times did Microsoft tank their earnings with failed attempts, until Azure brought success at last?) and the real inherent challenges from the Gulf's environment.
Another factor is that many of the Gulf oil states do not have free political systems, but are rather ruled by hereditary kings/nobility.
To buy consent from their population, they've put in place extensive welfare systems that disincentivize work from citizens. Hard labor is then performed by immigrants from poor countries, often under precarious conditions. While knowledge work is performed by expats, with generous living allowances under supervision from citizens who, reportedly, often don't really do, or know, much, having never performed grunt work themselves.
Another facet of buying political support is giving too much influence over school curriculum to religious authorities at the expense of teaching work skills.
Meanwhile, those citizens who are competent and highly skilled may very well wish to emigrate to countries with more tolerant social customs and participative political systems.
Given the lack of non-oil resources and small sizes, re-inventing themselves as Singapore-in-the-Gulf sounds attractive, but mostly they don't seem to have a local workforce with the skills to support that endeavour at this point in time.
Tourism is a possibility, but many people from outside the Middle East either dislike the restrictions on alcohol and sexual activity or disapprove of the migrant labor conditions used to support the tourism industry.
Ironically perhaps, a possible boost to their economy would be embracing large scale solar power generation and export as they have both the climate and empty lands to carry out it out.