Science and Arts are public things, promoting their benefit is for the public good. If the goal were about giving inventors a payday, they wouldn't be required

Science and Arts are public things, promoting their benefit is for the public good. If the goal were about giving inventors a payday, they wouldn't be required to disclose their inventions to the public at all, they'd just be given ownership of the idea forever. One could argue it was designed to help them both I guess, but when founding a nation, it's the nation and thus the public that you're looking out for. Giving a payday to inventors just doesn't make sense as a goal, but it makes perfect sense as an incentive to achieve a large goal.