It is hard to see that this would have been a positive thing in the long run. There were some Asian monarchies that persisted fairly late (Siam and Japan's until the present day, China's until the Communist Revolution, Malaysia (a rotating federal monarchy), Korea's until 1910), and those were generally positive in bringing about national unity and providing a centralize response to colonialism. But, in each of those cases, the monarch was unifying a genuine nation state or an indigenously created federal state.
In contrast, in 1857, it had been centuries since India was unified under a single monarchy, and was far from a nation-state. India was divided religiously, had a couple dozen languages, had a weak sense of national identity, and had a homegrown class of lawyers, senior civil servants, and politicians that was still very thin. A monarch is nothing without layer upon layer of well established aristocrats below him to legitimatize him and provide a foundation of elite support. A monarch without a long dynastic history that encompassed the entire sub-continent, or an aristocracy, would be hard pressed to rule.
India was precocious when it came to anti-colonial revolution, but if you look at the examples of Latin American revolutions in the 19th century, and the many grants of independence in the 1960s, for example, in Africa, again and again and again, the well meant initial independence regimes almost always collapsed amidst allegations of corruption and incompetence by the civilian administrations put in place, and the military regimes that intermittently followed were almost always worse. These were often followed by tin pot, cruel dictators who mismanaged their countries relative to the colonial regimes that preceded them.
When India finally gained independence, it was only after an adequate indigenous class of civil servants and lawyers was in place, and a lengthy campaign by unified political/protest movement had created a sense of national unity with grass roots support and a class of political leaders to implement the new government. Even then independent India soon divided into Hindu majority and Muslim majority regions in an event that was a apocalyptic national trauma with blood running in the streets, and in the Muslim part, coups and a national schism soon followed again.
It would only have been worse in 1857, for everyplace except perhaps a small kingdom in the region where the mutiny took place, with everything else fracturing (not that it was fully unified in 1857 under a consolidated British rule in any case).