I totally agree with your first point, and you lost me on the last sentence. Competition is a great data point, but just because you don't have any competition doesn't mean you aren't solving a real problem.
On the other hand, lots of people are solving problems which are not real.
I agree that finding a unique problem is possible, but it is more probable that you are missing something.
https://mastersofscale.com/peter-thiel-escape-the-competitio...
It's extremely rare to find a widely spread problem with zero pre-existing solutions or competitors in that field.