32% of fatalities (and I think less than 1% of critical injuries) are due to head injuries therefore in nearly 70% of fatalities a helmet doesn't even come in to play. Of the 32% many of them were wearing helmets (and over 90% in OZ) and still died of head trauma.

The rate of fatalities due to head trauma is still the same in the U.S., Australia, and Canada with very high helmet use as in The Netherlands with zero helmet use. Helmets don't appear to be doing anything. If helmets were effective then head trauma rates (e.g., head trauma as a percent of all bicycle injuries) should be much lower in countries with high helmet use.

MIPS was designed to overcome a flaw in standard helmets that was causing rotational injuries. EG, in certain crash scenarios, someone wearing a helmet received rotational injuries that they likely would not have if they were not wearing a helmet. These rotational injuries have resulted in death and permanent disability such as paralyzation. In these cases the rider would likely have been better off not wearing a helmet.

Do helmets make people feel more protected than they really are and lead to more dangerous maneuvers? Do they have any negative impact on sensory perception?

To me helmets don't appear to provide much if any positive benefit. And a number of negatives such as making your entire body hotter (and not in a good way), helmet hair, one more item to keep track of and complicate life. I'm not sure they provide anything beyond fashion (for people who think they're fashionable).

All that said, the safest helmet is the one you never need. Ride safely and work with local governments to build safe protected bicycle infrastructure.