Well, there are differences between those Empires and Austria-Hungary. For instance, nationalism in most parts of the world didn't get off the ground until the 19th and 20th centuries so the Romans and Persians didn't have to deal with that. And sub-Saharan Africa was still very socially (and otherwise) backward compared to Europe* and divided between feuding tribes which enabled the British Empire (and the French, Belgians etc.) to divide and rule between them. Organized resistance there with a united 'black' nationalism started much later.
*Note: I am NOT a racist. Denying the relative tribalism and social backwardness in 19th century Africa is not political correctness. Even today many African countries are burdened by feuding and backwardness (see the Congo for example).
The real point is the technological gap. There were African states with large-scale identities, but they were so hopeless behind in technological terms ("backward" is a relative thing: there had been great advances
in an African context since 1800) that the European powers could destroy them easily. Then the European powers played them off and exploited them,
creating much of the "tribalism and backwardness". It was simply a matter of technology and education. An empire which is all metropole has to educate its people and invest in their lands to prosper (and Britain had much earlier problems with Ireland, a metropolitan territory), but the Anglo-French overseas model was an exploitive one.
You're essential point is valid, but it has various common misconceptions about African history mixed in.
The Austro-Hungarian Empire was dealing with mostly well-educated Europeans who were aware of their equality to the Austrians and Hungarians, were very nationalistic, were unified with their own cultures and languages, were organized and able to voice their opinions well and fight together and therefore wanted a say. Giving the Czechs autonomy or even co-ruler status would make ruling the Empire much easier and I suppose the Austrians could set it up as the Kingdom of Bohemia tied in personal union to the Habsurg crown. It had existed well into the 19th century under Emperor Ferdinand I of Austria, making it a resurrection. IIRC, the Czechs composed another 13% of the A-H's population, giving the ruling groups a more comfortable majority of 57%.
There were some serious attempts to go through with this almost from 1867 onwards. The benefits were obvious, but the triicky issue was
German popular nationalism. In the pre-Italian War Germanisation era, all government officials in Czechia needed to know German. Nothing else was required. The upshot was that German was known to every educated Czech, but most of the Germans (concentrated in the recently re-Czechified towns and the Sudetenland) didn't know Czech. This meant that any change from the status quo, even the seeming compromise of requiring both languages, would actually weight the system in favour of Czechs, who were already bilingual (whereas requiring
either language was impractical in a bilingual country, and requiring Czech would have given the Germans fatal conniptions). This wouldn't have been at all unreasonable in a Czech state, but it generated outrage among the German community within whatever Austria-Hungary was (the Berlin government also picked up on the issue to attract nationalist support and increase influence over Austria) and so a triple-monarchy never made it through despite several attempts by the Vienna government.