Then it should be common for capital cities to seek to secede from the countries of which they are the political centres. But gosh, it's very uncommon. I wonder why that is the case.
Here's my theory. The people living and working in capital cities are smart enough to know that they owe the prosperity of their cities to the fact of their being political and economic centres. If London was no longer the home of the government would it remain as wealthy as it now is? Most people are intelligent enough to know that it would not. So they do everything they can to keep government there.
Secession is the very last thing that occurs to them. In fact, preventing provinces from seceding, not seceding themselves, is what makes most sense for them. And unsurprisingly that is what they tend to do.