Shouldn't the manufacturer of my monitor already know how it differs from the standard?
Any monitor worth the buying price will have a basic ICC color profile which should be downloadable from the manufacturer's website. (True of any device that produces visual output, including printers.) Usually the profile comes on a CD, which seldom escapes from its sleeve, so that the profile never makes it onto the computer. Worse, an ICC profile for the original monitor that came bundled with a computer may still be in place three monitors later, with horrible results. That's one reason on-screen colors in most offices are so ridiculously variable.
The ICC profile acts as an intermediary, to adapt the standard output from the OS, applications, or videos to the specific characteristics of that display, so that it will achieve some subset of the sRGB gamut (or something the manufacturer fondly believes is "pleasing"). Professional-grade monitors are often pre-calibrated for 100% sRGB and >99% of Adobe RGB. Less expensive graphics monitors and all office-grade monitors are not, and usually aren't capable of more than about 90% of sRGB.
TFT Central maintains a database of ICC profiles and OSD (on-screen display) settings for current and past models from most manufacturers. The ICC profile isn't the whole story, by a long way. You can wreck the color rendering by altering the brightness and contrast settings, for example, but the ICC profile will at least remove any hardware-specific peculiarities from the color rendering.
Simply installing an ICC profile doesn't mean you're getting a calibrated display, only that the monitor, when new, will give you something close to the manufacturer's intent. Color drifts over time for various reasons, so that recalibration is essential if you want to maintain accurate output.
Calibration, whether done with a full-on calibration tool or crudely by adjusting the GPU driver's output, creates a custom ICC profile that overrides the default. Color-critical work also requires taking into account ambient light in the workspace, and necessitates neutral colors in the area surrounding the display.
The perception of color is determined by range of variable factors that a device manufacturer has no way of controlling (or even determining). This includes the lighting in the room where the display is being used, if there's any natural lighting the date and time will impact color perception, the actual power being delivered to the display, the rods and cones in the eyes looking at the display, and even down to the neural receptors interpreting visual input. A color profile is really just a way of stating that in an ideal world, under ideal conditions, a device should show/interpret colors in a particular way. For most consumer displays, this would be the sRGB color profile or something quite close to it.
Environment, panel differences and panel decay. The environment affects the profile this can not be accounted for. The monitor panels themselves are different. Mainly because they change over time and they were slightly different to begin with. User settings may also be different, as you may be using different adjustments.
So the downloaded profile is some ideal average, that does not reflect what your monitor looks like. But rather what a new monitor of your make on the average looks like, in standard conditions.
Since the result decays and changes, you need to measure your settings regulary. Even continiously would be an option. Its not enough to make the profile once. So you see you really need an idividualized profile.
However, the downloaded profile may be better than nothing. But on the whole this subject is extremely convolved.