There are plenty of teeny tiny MOSFETs that can switch many amps due to their spectacularly low rds-on. The lower rds-on means less heat and thus the smaller package.
You need to look at rds-on vs Vgs (battery voltage if no divider is used) and Id vs Vgs. See at a particular Vgs, it allows a specific gate current to flow. If the load doesn't draw that much, then it acts like a closed switch except for a small rds-on. Higher Vgs and rds-on goes down slightly.
But, say your Vgs=6v when the batts are low, and the spec sheet says Id=1.5A for Vgs=6v but your driver- a switching driver- is supposed to draw current surges up to 2.5A due to its PWM circuit. Well, this is bad news because the MOSFET will instantly raise its resistance when current goes above 1.5A to limit the current to only 1.5A. Not only does that prevent the light from operating properly but will probably incinerate the MOSFET.
Note that a lot of garden-variety MOSFETs require >8v or even >10v to turn on fully. There are also ones which turn on fully at 5v, 3.3v, or even 2.5v. Also note that there are limits on Vgs, maybe 20v for the higher voltage gates but the low voltage gates may draw the line at like 8v.
Gates are very sensitive to voltage spikes. If you were to knock the case so the battery bounced off the contact for a moment, the inductive spike from the driver could create a positive or negative voltage that would destroy the gate. A zener diode on the gate (or some MOSFETs have internally protected gates) will keep it 100% protected.