That's interesting, I'm a bit confused, in this case high frequencies are not removed they are just quantized like all other frequencies. How is this reconciled with the assumption that high frequencies carry little information?
As far as the theory goes, the transform using the DCT is lossless apart from rounding errors. The quantization step just rounds more roughly. Which is where the lossy compression happens.
Basically you’re not removing the high frequencies because they carry little information, you remove the information they carry.
If you just remove the high frequency you end up with a blurred, smooth picture that doesn’t look like the original. But if you quantize the strength you get a pretty similar looking picture, apart from the degenerate case of sharp edges in a drawing.
Well it looks like a blurred, smoothed picture. This can be exploited during decoding if you want a smaller size than the original. For example if you only decode the 2x2 lower-frequency components of a 2000x1000 image, you get a nice downsampled 500x250 image "for free".
For example when making thumbnails this can be very useful, as for larger images you can often use just 2x2 or 1x1, dramatically cutting down the work needed for the final resample.
Oh and you can figure out what camera/software took a photo by looking at the value of n for each frequency. Everyone does it slightly differently to achieve different compression ratios.