I think those bits of information are closely tied to your browser functionalities. E.g. resolution, plugins installed. Keeping those bits for you would degrade your browsing experience.

Have a look at the parameters that bring the highest amount of fingerprinting bits in your config https://panopticlick.eff.org/ then see if it possible to disable them. I think it's just plain hard.

It's plain hard because the moment the browser blocks some of the fingerprinting techniques, the fingerprint developers will look for something else and move on. Just like spam and ads, it's an arms race.