Your problem is "quickly cooked" tomato sauce. The ingredients honestly don't matter at all (though I wouldn't use canned tomaters, if you do atleast buy a good brand). You genuinely don't need anything beyond Tomatoes and maybe garlic to make the sauce delicious. carrot, onion and celery are nice, but not needed. The whole point of a tomato sauce is to let it simmer for a long time, because only then will the tomatoes develop a more complex flavor. There are many techniques, but this one has been most succesful for me so far:
https://www.seriouseats.com/recipes...n-american-tomato-sauce-red-sauce-recipe.html
The secret to its deep, naturally sweet, complex flavors is to cook the sauce in the oven, allowing the surface to brown while the sauce slowly concentrates. The resultant sauce is great on pasta, with meatballs, on your chicken parm, or scooped right out of the pan with a spoon on its own.
This recipe needs five to six hours, however from my personal experience I notice very little difference in taste after three to four hours (I've done some tests) so that should be fine. Basically, a quickly cooked tomato sauce will always be too acidic, not sweet enough and just in general suboptimal in terms of taste. For me, there really are only two factors:
1. High quality tomatoes
2. Slow cooked for at least 3 hours, the more the better
Everything else is personal preference, really anything goes.
Aha. Tomato puree + soffritto, give or take. It's confusing to us because of
false friends: "mare" = sea, "marinaio" = mariner/sailor (think of 'marine'). We read marinata, we think fish or seafood will be involved. Anyway, would love to hear if what I proposed got approved.
Garlic/onion, butter/EVO oil, tomatoes is the fundamental tomato sauce in Italy, variations depending on personal taste and geography. Personally I'd call garlic a VERY personal taste in it, not standard anywhere at all: not saying it wouldn't work, but it's a whisker away from becoming another sauce entirely.
For some reasons Americans think literally every Italian dish contains garlic (or Parsley), it's a weird obsession I've never been able to grasp. Italian cuisine is the one that most perfectly shows that "less is more". Just think of carbonara or cacio e pepe, some of the best pasta dishes on the planet have only three or four ingredients.
I also agree with your assessment that the garlic is not needed at all. Just tomatoes and OO, or just tomatoes and butter is enough to make a good sauce.