The US strongly adheres to the separation of state and church, however it seems that the US cannot separate news and politics. Has this bias caused or contributed to the influx of alphabet news channels in the US, and why does the US differ from other nations like the UK, China, and Japan which all have a main broadcasting organization?
First, let's consider why the US has highly politicized news. The UK has media neutrality laws (NPR) that mandate neutral reporting. Japan has very strong defamation laws (Michigan Journal of International Law). These laws either outright ban or severely discourage highly partisan news stations. Chinese media companies are state-run and therefore unlikely to be critical of the state (for reasons that should be obvious).
The US, on the other hand, has a very high standard for proving libel against a public person, the so-called "actual malice" standard; that is, for a statement to be classified as libel in the US, it must be made with "knowledge that it was false or with reckless disregard of whether it was false or not. (New York Times v. Sullivan, 376 U.S. at 283)." Anything less is covered under the Amendment I freedoms of speech and press. This makes it very difficult to win a libel case in the US.
So while politics is a driving factor behind the proliferation of news media outlets in the US, the reason why it happens in the US and not in other countries you mention actually seems to be the strong protections of free speech and press guaranteed by the Bill of Rights.