15,000 per student is not "endless resources". To put it in perspective, it's less than half of what is spent on a student at an elite prep school, which I think is a more reasonable model for what cost-is-no-object education would look like.
But let's agree for the moment that not every student needs to have class sizes of four or five with a PhD instructors. I'd be very happy if every a typical student in Baltimore has $15,000 spent on him. But one thing you apparently didn't learn is the difference between "average" and "median". I pulled one of the elementary school budgets for Baltimore, and found that it was spending about 20% of its total budget on special needs personnel -- speech pathologists, psychologists, special ed instructors. Note that this doesn't include the fraction of regular teacher time taken up by this. So it's not unreasonable to assume that per-pupil spending if you discount the mainstreamed special needs kids would look more like $11,000.
I also note that you chose two of the highest cost places in the country to run a school as representative of the whole. Really, it's expensive to educate kids in NYC? Who'd a thunk it? As long as we're cherry picking, let me in the same spirit of fairness reach into the bag of scrabble tiles and "randomly" pick -- Mississippi. Mississippi spends close to the bottom of states on a per pupil basis, and is at the very bottom of the nation in student achievement.
Let's pick another state at "random" -- oh, look I got Massachusetts. Massachusetts perennially tops the list of states by student achievement by nearly every conceivable measure. But at $14k it's in the top quintile for per student spending . To a certain mentality Mississippi is getting a better deal because it gets away with spending only $7.9k/student. Specifically that's the mentality that isn't alarmed by the fact that almost 2/3 of Mississippi's eighth graders fail to meet minimum standards of proficiency and reading and math.
Here's a fun fact. The same percentage of Massachusetts eight graders score "advanced" by national standards for mathematics as Mississippi students score "proficient" -- 18%. How much would it be worth for the 18% advanced score to be *typical* of states rather than twice the national average? How much do you reckon it would be worth to pay on a per-student basis for the impact that would have on America's long-term economic prospects? Well compared to the national average, Massachusetts spend $3000/student more. That seems like a bargain to me.