you can be the safest rider in the world, ride only at the proper speed, only in the proper place, that place is always well maintained and everything else you can thing of.. All it takes is someone else doing something irresponsible and you are screwed..
i.e: a drunk driver loose control of their car, it invade the bike lane at high speed and hit you.. you are in for a bad accident that could be made a little less bad if you were wearing a helmet, even while doing everything you said..
now, if you are riding alone, in the middle of nowhere with zero change of someone else screwing it up.. then sure, you can skip the helmet, but if you are riding on road even if you do everything right you still at risk and helmet will improve your odds of surviving if something bad happen..
If you are on a separate / protected bike path (not on a road intended for cars), then there are no cars there, nor can they easily get on that path.
In practice such protections/barriers might range from moderately difficult to surmount (raised curbs ~ 50 km/h) ; nearly impossible to penetrate (row of trees, solid concrete wall, drainage ditch full of water ~ 80km/h); to outright having the bicycle path follow a different right of way altogether( >80 km/h ).
In general, the routes for cars, bikes, and pedestrians should be separated wherever there are large differences in speed that can lead to danger.
If you are riding
a) a safe commuter bicycle [1]
b) at safe commuter speeds [2]
c) on a safe separated/protected bike lane [3]
d) That is kept maintained in a safe state for the current weather
You probably don't need a helmet.
5) Yes, In other situations, you might want to consider it. [4][5]
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[ note: It turns out that implementing a)-d) are actually attainable in a fairly fiscally sustainable way (see eg.: Netherlands, Denmark), but it may need something of a turnaround in many a local government's safety culture ]
[1] https://en.wikipedia.org/wiki/Roadster_(bicycle)
[2] 12.4 km/h according to https://bicycledutch.wordpress.com/2018/01/02/dutch-cycling-...
[3] https://nl.wikipedia.org/wiki/Fietspad
[4] eg. when doing more dangerous activities like mountain biking or racing [5] or -of course- cycling in many places outside the netherlands or denmark. :-(
[5] https://www.cyclehelmets.org/1261.html "Why are Dutch cyclists more likely to be injured if they wear helmets?"
(edit: +references)