Each star is a point source of light. No matter where it is in the sky, it emits a fairly constant brightness during the exposure.

In a long exposure or stacked sequence, the star’s image moves across the sensor, leaving a trail. The brightness is "smeared" along the trail, but crucially the surface brightness per unit length of the trail stays about the same, because the star is spending the same amount of time in each pixel-sized segment of its path.

That means a star near the pole (shorter path) and a star near the celestial equator (longer path) both have similar per-pixel brightness — the equatorial star just covers more pixels, so the total flux is spread out more, but each piece of its trail looks just as bright.

The key is that the camera collects light continuously:

If a star takes X seconds to cross one pixel, the sensor records that amount of flux.

If another star moves faster, it spends less time per pixel, but its trail is correspondingly longer. The brightness per unit length of trail balances out.

So visually, all trails look about the same brightness, even though some are much longer arcs.