As far as I understand, aliasing comes from the fact, that you use a
bad sampling rate
Aliasing can also come from a 'bad' anti-aliasing filter.
So why is it you just don't use a fast sampling rate all the time
For the same reason that we don't use a sledge-hammer to crack a nut.
The problem isn't so much that the signal of interest is aliased, it is that high frequency, out of band information is aliased.
One approach would be to use an anti-aliasing filter to properly band-limit the input to the ADC.
Another approach is to oversample and then use a digital filter to reduce the bandwidth followed by decimation to reduce the storage requirements.
Another approach is a hybrid of the above.
Essentially, you don't want* to store any more samples than are necessary to properly analyze and reconstruct the signal of interest.
*Unless, of course, you're a high-end audiophile.