That's the classic way to think about it. Another way is to view the input as simply a sequence of voltage readings. Extracting a useful signal from that is an exercise in exploiting redundancy in noisy data. [1] Software defined receivers work that way.
Analog radio (AM, FM, etc.) is a hulking big carrier weakly modulated by the signal. Analog TV, which was AM video with FM audio, had 80% of the power in the carrier. Analog UHF TV stations often had multi-megawatt transmitters to overpower noise by sheer RF output. Digital broadcast TV transmitters output maybe 150KW, because the modulation is more efficient.
Modern modulation techniques are insanely efficient. It's amazing that mobile phones work.
[1] https://ocw.mit.edu/courses/6-450-principles-of-digital-comm...