Who says there are no targets in 2nd island chain distances, don't just look east, look west, look south.
Remember that a Shaheed already has a 2000-2500km range when launched from a truck.
That covers pretty much all the land targets that matter.
The South is actually pretty friendly, until you reach a handful of bases located in Australia.
Looking West, China shares land borders with many countries, which are not realistic threats.
China can project power just from within its border to Europe, Middle-East, Australia, SEA, all within range of long range missile or PLA bombers with standoff missile. China's location is its biggest advantage and the biggest curse. They are located in the center of Asia, which is the part of the world with the most amount of people in the world, most amount of land, most amount of resources.
Which means China has the most amount of potential enemies but also it can gain the most amount of dominance just from within its own borders.
If US can claim western hemisphere as its backyard, China can start to claim Eastern hemisphere as its own. Just by using its air force and rocket force.
The thing is, what core interests does China have?
In these regions it is mostly about trade, not military dominance and vassals like the USA.
But let's say China does have military dominance to a distance of 2500-3000km from its borders to the Middle East. That covers all of the Persian Gulf. But what then?
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In the Middle East, we basically have a situation where there are many tribes always squabbling and fighting each other.
Then you have the religious dimension, with fanatics in charge of a Muslim Iran, Jewish Israel and Christian USA - essentially fighting over Jerusalem and Palestine as a holy land. It's not an exaggeration that they all think they are doing God's will, but remember they actually worship the same God.
So what does China gain from building a dominant military and then using it in the Middle East?
But having said that, with what China has to build anyway in terms of military capability for the Western Pacific, this can be redirected to the South and West, if really required.
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I also think that India is too big for China to dominate