The reasons are different for the two examples.
Finance Company and Insurance Company
The reason you wouldn't use "one" in this scenario is they are compound nouns. An "insurance company" is two words for one thing. "Insurance" isn't an adjective describing "company" but is a noun being used in coordination with the noun "company" to form the compound noun "insurance company." The same is true of "finance." The adjective form of the word is "financial," but the noun "finance" is being used with the noun "company" to form the compound noun "finance company." You would no more break up the compound noun "insurance company" to say "insurance one" than you would break up the compound noun "firetruck" to say "fireone."
War Film and Horror Film
You actually could use "one" with these terms, but the way you structured it makes it confusing. It's not clear that "one" means "film" there if you say "horror one," especially since earlier in the sentence you say "on 'one' channel," making "one" sound like it maybe means "channel," like "horror one" could mean "horror channel." It's not that people couldn't figure it out, but needing to makes the phrasing awkward. Anyway, that's why most people wouldn't use "one" after "horror" in that sentence, because it's not clear. Here are some example of how it would be used:
- "There were two films on, a war one and a horror one."
- "There was a war film on ABC and a horror film CBS. I watched the horror one."