I guess you could argue that that's the reasoning behind the progressive tax regime. Australia's progressive tax lines up with the low end of that but if you were going to claim that the tax free threshold was to cover general living expenses then it's going to need to be a lot larger, 20k bere is not enough to cover rent, food and utilities here, a 3x2 near Perth is like $800/week for rent and I would argue interest on a mortgage is comparable and Perth is on the cheap end of Australian cities. That's like 40k without utilities and food. So either the tax free threshold was poorly implemented without indexation against inflation and cost of living or the driver of it isn't to cover basic cost of living and is more to ease the burden on the poor end of town. I guess you could say it's a little bit of both but arguably indexation should be implemented.

Standard deduction is slightly different than an exemption. You're deducting a set amount (instead of itemizing it, which only makes sense to do if the total is more than the standard deduction, which it won't be for most professions).

An exception exemption would be removing a portion of the taxable income before it is taxed.

Pretty similar outcome for most people, but still an important distinction.

Edit: fixed autocorrect error