The exact time someone has observed or is observing organisms at a particular location is a pretty detailed piece of personal information to share publicly.
Yes, iNaturalist isn’t a place to store completely private data. But, like the option to obscure or hide locations, some may feel more comfortable participating if there were an option to automatically hide the exact time observations occurred. Timestamps can already be removed manually from individual observations. It is, however, moderately more burdensome to remove timestamps from photo metadata, which is shared with other iNat users.
I foresee this being an opt-in account setting.
Although time of observation can be useful data for some research, I don’t foresee there being the same level of demand for a trust system to allow particular users to view your time observed, like the existing feature for sharing private locations. Requesting that data on a case-by-case basis is probably sufficient.
It’s not quite as important to hide “Time Added”, except for the case of people who are observing with the app and have not turned off auto-upload.