The following description might be boring to native speakers of English, but I would like to hear your opinion.
According to Longman Dictionary of Contemporary English, “the” is
“used before nouns referring to actions and changes when they are followed by 'of':
‘the growth of the steel industry’
‘the arrival of our guests’”
I understand the above basic rule.
As you have found, this rule is either wrong or incomplete or must be considered in the context of all the other rules they give. Or perhaps you are misinterpreting the phrase "is used".
For example, " 'the' is used" can mean:
1. You can use "the" in this context. (This says nothing about whether you can use other words like 'a' here.)
2. You use "the" in this context only. (You can't use "the" in other contexts.)
3. You can only use "the" here. (You can't use other words here.)
4. You must use "the" here. (You can't use the zero article.)
5. "The" is often used in this context. (But need not be).
You seem to be assuming that " 'the' is used" means 3. or 4.
Looking at the list in Longman's, I think it means 1. or 5.
What confuses me is that the following sentence appears in the same dictionary.That's correct too.
‘The killings are part of a campaign of elimination of the political opposition.’
Native speakers of English can intuitively find whether “the” is required or not, but I am not a native speaker of English. I need to find some rules.If you read a lot and often see 'a' in situations where a rule that you have learnt says you need "the", then you have probably misunderstood the "rule", or even what the nature of rules actually is.
Rules are a poor substitute for experience or inductive reasoning - both of which, I concede, take time.
Then I came to a hypothesis that in the above sentence, “campaign of elimination” almost sounds like one word and that is the reason “the” is not required,
Ingenious, but wrong.
Certainly "campaign of elimination" (a noun followed by an adjectival prepositional phrase) is functionally a self-contained phrase, but that has no bearing on whether "the" or "a" or the zero article is needed for it.
and moreover, “elimination of” can be replaced with the ing-form “eliminating,” i.e., ‘The killings are part of a campaign of eliminating the political opposition.’ I guess that “the” may be omitted in such “of-phrases.”
Yes, that's right.
According to my hypothesis “The port has stopped acceptance of mail” is fine.
“The port has stopped the acceptance of mail” is fine, too. The “acceptance” can be replaced with the ing-form “accepting.”
Is my guess wide of the mark?
Your hypothesis is wrong, because it doesn't explain what you claim it does. Otherwise you are right on most counts.