At the modern complexity and importance of science, we do need to put much more emphasis on checking whether it is done right. The original vision of the Royal Society involved rigorous peer review, to the point of demanding scientists to demonstrate their experiments in front of their peers: https://www.sciencemuseum.org.uk/objects-and-stories/17th-ce... The curator of these literal peer reviews held the first paid position in science.
Journals do have the profits to hire or otherwise pay peer reviewers full time. They would become experts in their field in the process, and thus more suited for the task than the ones in the current system, where even undergrads are asked to review for high-profile outlets like NeurIPS. Also, full-time rigorous peer reviewing would be an interesting career prospect for many current scientists. And here is your startup idea..