Because in general we tend to be OK with wearing helmets for sports when doing so seems a reasonable tradeoff but not for day to day activities. Clearly helmets would be beneficial for certain types of injuries but it's hard to imagine many people willing to make the tradeoff. (I would also wonder if they'd actually be a net benefit given potential reductions in visibility, etc.)
Cycling (in the US) sort of falls between those two categories but, at least for adults, many who use bicycles as transportation also use them as a sport.
So would 5-point harnesses, but almost no one has those installed in their car.
Safety is usually about going after the lowest-hanging fruit: making improvements that have the biggest net benefit. In cycling, head injuries are common because of how the rider is exposed and how they frequently fall and what kind of surfaces they're likely to impact. In car driving, not so much; the biggest benefit in car driving is to keep the body anchored to the seat so that it doesn't fly into the dashboard or steering wheel or anything else, so that's why we wear seat belts. There's still problems with body parts hitting parts of the car, so then we added airbags. There's still problems with getting whiplash, so now we have seats and headrests designed to minimize whiplash injuries. It just isn't often that you hear about someone getting a head injury in a car wreck in a modern car; I can't think of ever hearing of such a thing in fact.
Also, the speeds people reach on city streets aren't as high as what race cars reach, and in most auto racing, helmets are indeed required. However, the helmets used in auto racing (full head-covering types) also negatively affect visibility, which is very important in city driving, and not that important in racing where the conditions are far more controlled and you don't have to worry about random pedestrians or bad drivers all around you.
It's not like we don't have safety devices in cars; we do, and in fact we have many of them and they tend to be rather expensive and highly-engineered. 3-point seat belts with pre-tensioners, multiple airbags (front, canopy, A-pillar, seat side), anti-whiplash head restraints and seat mountings, etc. They also tend to be passive in nature: only seat belts require you to do anything to make use of them, the others are just waiting there until they're needed. As a society we've put a lot of money and effort into reducing deaths and injuries in cars, and it's paid off well. We could go further with helmets and 5-point harnesses, but how much benefit would there be, and how many people would refuse to use them? (BTW, there's an argument against 5-point harnesses, that they shouldn't be used unless a car has a roll cage otherwise your head can get crushed in a rollover, whereas with a 3-point harness your torso just moves to the side towards the center if the roof caves in.) Oh yeah, don't forget what we do with kids these days: they have fairly elaborate child seats they're required to sit in, which they really are anchored into.
