Hypothetical fantasy? It is the Alabama system. But yes, it would be. Alabama's business and law programs are far superior to Pitt. Pitt med/nursing education is a bit better than UAB. The rest of the schools are either inconsequential and/or slightly better than the other. It is ridiculous for anyone to think Pitt is vastly superior.
UA and UAB are in the same system, but so are UNC-Chapel Hill, NC State, East Carolina, etc, similar to UCLA, Cal, and UC San Diego, etc., similar to UT-Austin, UTEP, and UTSA, etc. They are completely different schools, same system or not. You can't just combine them, and no federal or accrediting body looks at them as the same institution. And undergrad students in Tuscaloosa certainly can't take advantage of the medical and research facilities available in Birmingham, or vice versa.
Outside of Law, and Pitt’s law school troubles have been much discussed on this forum as completely unacceptable, you’d be hard pressed to find an academic program better regarded at the entire UA system.
Pitt’s Katz Graduate School of Business is actually ranked #53 in US News, and UA's Manderson is ranked #54. Pitt's undergraduate business program is ranked #38 overall (#24 public). UA's is #63 overall. In Bloomberg’s undergrad business rankings, Pitt is #49 and UA is outside the top 114. P&Q Pitt is #40 undergrad, UA somewhere outside the top 50. Financial Times global MBA Pitt #85 (#45 US), UA not ranked. The Economist MBA Pitt #55, UA is outside the top 96. I could go on.
Overall, UA-Tuscaloosa is ranked #103 by US News for undergrad rankings (#46 public, #431 global). UAB #159. PItt is ranked #68 (#24 public and #47 global), and this is among its worst rankings. If I went into the more comprehensive rankings that include graduate metrics, it is a complete beat down of either UA school.
Here are some other programs from US News...
Undergrad engineering: Pitt #50, UA #105
Grad engineering: Pitt #42, UA #104.
Education: Pitt #27, UA #93.
Information Science: Pitt #10, UA #28
Public Affairs: Pitt #35, UA #130, UAB #68.
Nursing: Pitt #8 & #7, UAB #13 & #23.
Using 2016-17 Common data sets, admission standards number greatly favor Pitt over UA-Tuscaloosa: SAT CR+M Pitt 1285, UA 1105; freshman in top 10% of HS rank Pitt 52%, UA 37%; average GPA Pitt 4.14, UA 3.69; 6-year graduate rate: Pitt 81%, UA 69%.
Bio and health sciences blow UA-Tuscaloosa away, and are significantly better than UAB, which is a very good institution and I actually have friends on faculty there.
Pitt’s Med School is ranked #15 in research and #13 in primary care. UAB is #35 and #31. Similarly, in dozens of the other health science programs, like public health and PT, are substantially better regarded than UAB and I won’t take the time to actually list all the numbers. But the most important number is NIH research funding. For FY16, Pitt receive the 5th most allocations in the nation of any medical research institute at $476 million. UAB was #25 with $238 million. That means Pitt gets double the medical/bio research funding just from NIH, which is the most prestigious and telling source of funding. They're not that close, at all.
Pitt is a LOT closer to elite than most people realize in many areas, and in some field, actually already very elite.
Again, you were absolutely right about your last line above. It
is amazing.