It is valuable for a simple reason: it applies to the largest charges on the bill, and it is the one line of arithmetic a landlord does not expect a tenant to do.
Why you do not owe for a new floor
Carpet wears out on a schedule whether anyone damages it or not, and landlord–tenant guidance typically assigns it a useful life of about five to ten years. Once that life is spent the carpet is worth roughly nothing: it was going to be replaced regardless.
So if you damage a carpet near the end of its life, the loss you caused is small — the remaining years, not the replacement price. Making a tenant pay for a new floor on an old one is called betterment, forcing you to upgrade someone else's property, and it is widely disallowed.
The arithmetic, worked
Say the carpet costs $1,400 to replace and carries a seven-year life. That is $200 of value used up each year. If it was six years old when it was damaged, one year — about $200 — was left, and $200 is the most that can fairly be charged.
A statement billing the whole $1,400 is therefore over-charging by $1,200 on a single line. The same logic scales down: a damaged bedroom is a fraction of the flat, not the whole job.
It is not only carpet
Interior paint depreciates fast, often over two to four years, so a full repaint billed after a three-year tenancy is usually turnover the landlord owed anyway. Appliances, blinds, worktops and flooring all carry useful lives of their own.
Any line on an itemisation that reads like a brand-new replacement is a line to age before you accept it.
How to raise it
In your demand letter, take each replacement charge and state three things: the item's age, its typical useful life, and the prorated figure you actually owe. Then ask for the difference back.
You do not need the landlord's receipts to make the argument — you need the age and a reasonable life estimate. Landlords rarely expect a tenant to arrive with that, which is exactly why it works.
One caution
Informational, never legal advice. Useful-life schedules vary by state and by the guidance a court follows; the figures here are typical illustrations, not your law. For a dispute that matters, talk to a tenant lawyer or your local legal-aid office.