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I shoot a lot of macro images with flash and custom light mods. Most often I set my camera to F/18 and 1/200 of a second with 1/4 flash power.
Every time the light changes I need to adjust my ISO. I've tried AUTO ISO but since I'm focusing very close, the camera doesn't get the exposure metering right with my flash and light mod.
I wonder why the camera can't apply AUTO ISO after the image was taken such that the image get the right amount of brightness?
Because ISO adjustment changes the gain applied to the analog sensor signal before digitization.
Whether that results in better performance vs. a brightness adjustment after digitization is not necessarily given, (see steven-kersting's answer about ISO invariance), but in many cameras it is different.
If you have an ISO invariant camera, you can indeed forget about setting ISO if you're going to post process anyway.
Addendum: I should add that the setting "Auto ISO" at least in some cameras can set the ISO value to "non-natural", i.e. non full stop (doubling/halving steps) values, eg. 125. These values may not be available for manually selection and are actually digital expansions from the nearest real value. (I'm talking from experience with my entry level Canon EOS here, YMMV)
In fact, ISO (auto or otherwise) is applied to the sensor readout after the image is taken; but the camera has no way to review the image to determine the exposure is correct (and what is correct anyway?).
These days there are a lot of cameras that are very nearly ISO invariant. And with one of those cameras it is possible to leave the ISO set to minimum for all images; and then brighten them in post, with negligible impact to the results compared to the camera increasing the brightness with auto ISO. Effectively, you can change the ISO in post with essentially the same results.
This chart shows the benefit of using a higher ISO as light levels decrease for a Nikon D750, and Olympus EM5, and a Panasonic GX-9 (there are many others with similar performance)... around half a stop of improvement on the chart is about the minimal limit detectible visually.
@ths answer is spot on about Auto ISO but also about ISO. This gain is applied on the sensor-readout before being digitized. Since the Analog-to-Digital conversion has limited bit-depth, the process is not reversible.
Auto ISO has another effect in that the selected ISO on most cameras except in Manual mode will affect other parameters. So if you allow the camera to use a higher-ISO automatically, it could also change aperture, shutter-speed and flash output. None of these can be changed after the fact and so it would be impossible to apply the Auto ISO behavior.
You can. ISO on a digital camera is the same as a brightness adjustment post capture, because the ISO of the sensor is fixed -- it's a function of the design and manufacture of the sensor itself. So ISO shifts are done by brightening the image after it's taken (see below for a caveat to this).
You can leave the ISO at the natural ISO of the camera and brighten images yourself in post. In general, I see that cameras do a better job with Auto ISO in-camera vs. dialing up exposure in Lightroom, as the camera handles noise better. But your mileage may vary.
Some recent cameras/sensors have "dual gain" capabilities to offer different base ISOs. E.g. my Fuji XT-4 base sensor ISO is 160. It also has a "high gain" sensor mode that kicks in at ISO 800. All other ISO values are emulated in-camera by brightening the image post capture.
