Driving, gymnastics, break dancing (ESPECIALLY break dancing)… Anything that can’t be timed or measured or otherwise objectively decided should be removed from competition.
How do you quantify “style”? How do you ensure there is not biase from judges based on their knowledge of the competitor, be it country they are representing, or personal connections, or racial / religious opinion? How do you fairly compensate for what your personal opinion considers “worth” more when it comes to a trick or routine compared to another?
Swimming, running, jumping, throwing things a distance are all things that can be measured and ruled against a standard that every competitor uses. It’s fair and it’s removed from any bias.
The Olympics are supposed to be about competition between athletes and shouldn’t be affected by popularity or politics, which anything with an interpretive aspect to the result will suffer from.
So yeah, remove the feels sports and limit the Olympics to reals sports.
Deciding upon a distance, starting method, surface, and season for the race all introduces subjectivity
Variation in objective race conditions does not equal subjectivity. People can have subjective preferences about what type of race would be best to run, but once decided, the outcome is objective. One person factually reaches the finish line first. They are objectively the winner.
What about point deductions for faults, like a minor collision or improper cornering? It happens in (for example) motocross all the time. It’s not like there aren’t other criteria.
Everything you mentioned can be rigorously defined in terms of time, position, velocity, angle. If, in a certain race, the rules are poorly defined, or if the relevant information is not known to the judges with sufficient precision and accuracy, or if the judges are incompetent, then sure, subjectivity could be introduced into some particular race. But it is possible in theory to eliminate subjectivity from racing, if care is taken to do so. It is not conceivably possible to eliminate subjectivity from an aesthetic judgement about “style.”