In the top countries, teachers are paid like doctors and treated with much greater respect and autonomy. That shouldn't be surprising as being able to attract and retain the best talent is critical in any industry. We lose 50% of teachers in the first 5 years of their teaching. These are often the best ones, who go back to grad school and change careers to support their families.
While throwing money towards new educational "innovations" rarely pays off, paying teachers more directly would. I've often said that if they proposed raising my taxes with a guarantee that the money went directly to teacher salaries, I'd do it in a heartbeat. That's the best way to improve schools, because the factor most correlated to student success after family/economic demographics is whether they have a good teacher.