That is a common misconception, but bears no resemblance to reality. As the other commenter noted, incognito mode (for any browser) only concerns with the local machine.
What you mentioned, "minimize traces of activity left behind on other computers as well", is a difficult task. Attempting to do so requires more advanced techniques that entail tough compromises. Consider using Tor, you are anonymous to the endpoint (e.g. the website you visit does not have your IP), but confidential data is not safe from prying eyes in the process. Alternatively you can use some sort of crypt to sign and encrypt your connection... your data is safe from prying eyes (potentially verified as well) but you are no longer anonymous. This can all be mitigated to some extent, but it is well outside the scope of a browser.
> Count the motivations to resist alterations that would doubtless improve Chromium's respect for privacy.
That's a very indirect way of explaining motivations. I am certain that there are conflicting requirements that have tradeoff and not as black-and-white as you make it seem.
Firefox is a great contrast to Chromium since they are likely to have greater respect for privacy. Is there a privacy aspect that Chromium lags significantly behind Firefox? If not, then your hypothesis (on motivation) is wrong (proof by contradiction: Mozilla doesn't have the same motivations)
What you mentioned, "minimize traces of activity left behind on other computers as well", is a difficult task. Attempting to do so requires more advanced techniques that entail tough compromises. Consider using Tor, you are anonymous to the endpoint (e.g. the website you visit does not have your IP), but confidential data is not safe from prying eyes in the process. Alternatively you can use some sort of crypt to sign and encrypt your connection... your data is safe from prying eyes (potentially verified as well) but you are no longer anonymous. This can all be mitigated to some extent, but it is well outside the scope of a browser.