One element is that the UAE was not really a colony, it was basically a protectorate. Its precise legal status was left incredibly vague right up until the very final years before independence when some of those issues started to be or had to be resolved (for example, the borders of the emirates were always quite vague, something that had to be and in large part was clarified prior to independence.)

Other former British mandates and protectorates had similar systems. Iraq before 1958 likewise had a King. Jordan still does. The head of state of Bahrain recently promoted himself in 2002 from being an emir to being a King. Oman, another British protectorate, has a Sultan. None of these countries are in the commonwealth.

So in that sense it's hardly unique. As to why other colonies like India or Pakistan did not end up with a monarchy, that's not at all my area of expertise but as far as I'm aware it has mostly to do with the fact that upon independence they decided to form republics, which effectively meant the end of the princely states, without which perhaps there might be monarchies in India. As I say, that part is beyond my area of expertise.

As for the state formation of the UAE, I've only skimmed the first hundred pages or so but I'm quite a big fan of Kristian Coates Ulrichsen's new book The United Arab Emirates: Power, Politics and Policy-Making.