This is what intuition suggests, and is indeed what happens point-blank when the beam is just exiting the light. However, if the target is far away, the wider reflector actually gives you a tighter and more intense hotspot! The beam is initially thicker but less divergent, so over a long distance the lower divergence outweighs the initial thickness.
It might help to have a schematic drawing of what a wide reflector beam (red) and a small reflector beam (blue) look like, point-blank (left) and at a distance (right):
Incidentally, what you stated is exactly the reason why a super thrower like BLF GT can’t burn something point-blank, while a much floodier light like a S2+ triple can.
The fact that emitters are not perfect point sources is the reason flashlight beams aren’t perfectly parallel (and don’t have infinite candela) like the red beam from the above illustration. Without going into the weeds: for a fixed reflector, the size of the hotspot at a distance is roughly proportional to the size of the emitter.
If you’re interested in the weeds, here’s a simulation I built that lets you input the reflector geometry and emitter size, and outputs a simulation of what the beam looks like at a distance, hotspot and corona and spill. Calculator for reflector beam profile