I have always made my pizza sauce very simply. Pizza sauce is not pre-cooked. It is just tomato. In fact, if you go to Italy you may find the sauce with salt and pepper, but basically it is just plain tomato. You can blanch whole tomatoes, peel them, cut them across on the horizontal, squeeze out the seeds and puree the flesh.
You can use crushed tomato.
They usually just spread the sauce and sprinkle with a few basil leaves and mozzarella slices.
Sometimes, I have people who like rather sweet tomato sauce on their pizza. Sicilian pizza is this way. In this case I dilute a can of tomato paste with water, after adding salt, pepper, 2 parts Oregano, 1 part Basil, garlic or garlic powder and red pepper.
After thinning, it should be about the consistency of heavy cream.
Smell the finished sauce and give it a taste before using it.
You may also just use the thinned paste, salt and pepper.