Indeed, it's sometimes impossible to know if the area is indeed what is reported, or even a less figure - and if less than reported, then for how much. Reason for this is simple: if sea ice has "holes", "srtipes" etc of open water in it which are significantly less (in size) than maximum-possible resolution of the recording apparatus (say, a satellite), - then there are simply no direct means to detect it. With much of sea ice slushed, churned, mixed etc (say, by a huge cyclone or two) - this becomes especially significant issue.
There are probably some indirect methods to detect that the ice is in fact seriously less than 100% concentration even if "holes" are too small to be directly detected and measured, - i don't know, i am no specialist, - but i bet such indirect methods wouldn't always work.
So yep, extent is much easier, can be calculated rather precisely directly from observations. However, many critically important physical processes are in fact dependant on ice area (and might i say, not on reported/calculated by modern means ice area - but on real one, which accounts even for holes/breaks of extremely small size, say, millimeter-wide). Among such processes, i guess, are evaporation, local albedo change, patterns of methane emissions (even small cracks/holes let lots of methane go out stright up - otherwise methane piles up under the "impenetrable" ice, which has its own effects, sometimes large-scale), mechanics of ice packs/fields movement - and most likely some other important processes. That's why, i guess, sea ice area, even while it can't be measured exactly precisely, is still very important to science.
Please correct me if i was wrong somewhere. Thanks!