The missing piece is that a sensor pixel doesn’t really give you a strong, instantly useful voltage. A photodiode primarily generates charge/current when photons hit it. That charge is collected in a tiny capacitor or “well,” and the camera measures the accumulated charge after some time.

Exposure time is needed because the signal from light is very small, especially in dim scenes. If you read the pixel too quickly, the useful signal may be similar in size to read noise and other electronic noise. Letting the pixel collect photons for longer improves the signal relative to noise.

So a digital exposure is essentially a counting process: brighter areas fill the well faster, darker areas more slowly. At the end of the exposure, the stored charge is read out and converted into a pixel value.

In principle, you could try to read almost instantly, but that would be like using an extremely high ISO: very noisy unless the light is very bright or the pixels are very large. Some sensor ideas involve multiple readouts during one exposure, but standard cameras still rely on accumulation because it gives a cleaner, more useful image.