In principle, a camera could capture many short samples and combine them later, but current imaging systems are limited by two big issues: sensor readout and image quality.

First, full-sensor readout is not instantaneous. Most sensors are read line by line, and reading an entire sensor hundreds or thousands of times per second requires far more bandwidth and processing than typical still cameras can handle. It also creates huge amounts of data.

Second, every read adds read noise. A normal exposure integrates light continuously and is read once, so that noise is introduced once. If you split the exposure into many tiny reads, read noise is added repeatedly, which hurts image quality.

There is also a photographic reason: shutter speed is not just about total brightness, but about defining a slice of time. A true 1/1000 s exposure freezes motion in a way that a 1-second capture processed afterward generally cannot fully reproduce if moving subjects have already blurred during each sample.

Some modern cameras do related things in limited ways, such as video, HDR, or computational photography, but not as a full replacement for normal shutter-speed control.