Sleep restriction is the piece of CBT-I that people argue with. You are already exhausted, and the method asks you to spend less time in bed. It is also, in the research, the single most powerful component of the whole approach.
The logic is simpler than it looks. Someone who has been sleeping badly for months tends to respond by going to bed earlier, staying later, napping when they can — reasonable moves that have the effect of spreading a small amount of sleep across a large amount of time in bed. The bed stops being a place where sleep happens and becomes a place where lying awake happens. Compressing the window does two things at once: it builds up enough sleep pressure to make sleep come faster, and it stops the bed being associated with frustration.
What almost nobody writes about honestly is the first fortnight. Restricting time in bed increases daytime sleepiness before it improves anything, and that is not a side effect of doing it wrong — it is the mechanism. It is also the point at which most people stop. The articles below cover the arithmetic, what to expect week by week, and when this approach is the wrong one for someone entirely.