Are there any disadvantages of having a “free fall sensor” on a hard disk drive?
Nope.
if it's necessary to have differing physical dimensions between free fall sensor drives and those without, e.g. does it make it any thicker, and therefore reduce the systems where it can be installed - particularly smaller laptops?
No. As you can see, even a typical 2.5" laptop drive has enough space for the tiny component.
does it actually make the system less reliable - because of false alarms whereby the drive thought the laptop was falling but it wasn't?
Not generally, no. The sensor is specifically calibrated to detect free fall (like the laptop being dropped), not just minor bumps.
If a laptop is dropped, it will experience a a moment of weightlessness and then a sudden and relatively massive increase in shock (g-forces). For hard-drives in which a head is floating on a microscopic cushion of air above a disk spinning at thousands of revolutions per minute (Scott Mueller analogized it as a jumbo-jet flying a few feet off the ground), this can be/is usually quite harmful and results in a catastrophic head crash.
Hard-drives (usually laptop drives) with free-fall sensors are designed such that when it detects that the drive is falling (usually the whole system), then it tries to park the head(s) quickly so that when it hits, the heads are on a non-data section of the platters. This by no means guarantees that the drive will survive; it can still kill it if the shock is severe enough, but at least the platters will still have their data intact (unless the shock is somehow astronomical enough to actually jolt the magnetic bits around).
If the laptop is merely bumped, then the sensor should not trigger since it is calibrated not to. Instead, what may happen if the bump was hard enough and the drive happened to be active at the moment is that it will encounter a read or write error and log it in the SMART table: G-sense Error Rate: The count of errors resulting from externally induced shock & vibration.
Usually however, it will just try the read/write again and unless you see other, more critical SMART values rise, then nothing particularly bad happened.
I suppose that the fact that a manufacturer produces both drives with and without free fall sensors says something about possible disadvantages.
Or it is just a way to sell a more expensive model.