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Everyone entering the UK without 'Right of Abode' (or similar rights) is subject to an inspection by an Immigration Officer (paragraph 2A of Schedule 2 to the Immigration Act 1971), or in vernacular, a "landing interview".
An IO has broad powers handed down from Parliament that extend well beyond the immigration rules. They are empowered as agents for HMRC, the National Crime Agency, the Children's Act, the Human Rights Act, and other just about anything else that endangers or affects public welfare.
So they are entitled to conduct a landing interview and to ask anything they want and to see evidence for any statements that have transpired. Moreover, they are empowered to detain people who have not produced sufficient evidence.
Having said that, let's turn to your question...
It just seems unnecessary and I have not found the site that says "carry all the same documents for the border entry point".
Here's a screen cap from the relevant site...
You can reach this site by following the wizard at Check if you need a UK visa
Note that this is not a rule. Instead it is guidance only. The massive bulk of arrivals do not carry evidence and never get challenged to produce it. Notwithstanding this, it is an act of prudence and sagacity to prepare yourself to back up ANYTHING liable to arise in a landing interview. This includes financial evidence, hard evidence of onward travel, employment contracts, along with the more exotic evidence like children's birth certificates, marriage certificates, unusual luggage, notoriety, criminal history, and the like. They are entitled to ask for evidence if they want and it's all part of "what is". And they can detain you until you produce satisfactory evidence. Even Brits are subject to portions of the landing interview.
I always write to carry your evidence because it is "best practices" for a traveller (of any nationality).