If income tax was not progressive, is there any reason to believe laborers would just get paid more to make up for how much they get taxed?

Isn't that way electricians make more in SF than they do in Memphis Tennessee? Isn't that why engineers get paid more in California, but have to take a pay cut if they work remote from Ohio?

This makes me wonder how effective the progressive tax system is.

Im not familiar with the tax system in the us, but progressive, direct taxation is indeed progressive. Usually this is offset by The regressive effects of indirect taxation, fees for public services, education, fines and so forth.

It's easier to make income tax progressive with tax bands.

It's orders of magnitude harder to do it with consumption tax. The tax authorities essentially have to form an opinion on the "luxuriousness" of each good. That's a monumental administrative pain.

This is a feature, not a bug, if you come at it from the perspective of somebody creating or exploiting tax loopholes (I.e. you're bill gates).