They can—and some cameras do use sensors larger than full frame. But bigger sensors bring major trade-offs.

A larger sensor costs much more to manufacture, and it usually requires a larger camera body and larger lenses. That increases size, weight, and system cost.

Also, a bigger sensor does not automatically make exposure settings magically better. If you scale the whole camera/lens system up, total light collected increases, but it is spread over a larger image area. Much of the real low-light benefit comes from larger pixels (or lower pixel density), which can reduce photon noise, not simply from sensor size alone.

Sensor performance is also limited by other factors such as read noise, thermal noise, and lens sharpness. Making everything larger can increase bulk and optical challenges, and for equivalent framing and depth of field you may need bigger, heavier optics.

So the answer is: larger sensors do help, but the gains are balanced against cost, lens size, camera size, weight, and diminishing practical returns. That’s why full frame is often a popular compromise, while medium format and larger systems exist for cases where the extra size and expense are worthwhile.