Hi,
In general using a browser or any other software that accepts input on a public computer is never safe because the data can be hijacked at so many levels.
Chrome indeed has some mechanisms to make it easier for users and administrators of such machines to use the browser safer - starting with Incognito mode for users so that the data entered in the browser is not stored on disk. The administrator can adjust the links to chrome to always start in incognito mode for example. A few administrative policies like "Disable Sync" or "Force ephemeral profiles" can make the browser safer even with non-incognito profiles because the data is guaranteed to not leek outside of the started browsing session. Eventually since Chrome can not control the OS and the hardware this is only a soft guarantee anyways.
Much better guarantees are provided with ChromeOS running in the special "Public session" mode where data is stored in a way that can not be extracted without tampering with the casing of the machine. Also those sessions have automatic expiration timers so that even absent-minded users that simply walk away without signing off can be sure that unless somebody is stalking them will have their data cleared after them.
I think you as a more tech savvy user can help to improve the situation by raising awareness of the issue to the organizations owning such machines and demanding a better solution than the current one.
Cheers,