For example, the list below is the largest cities without a single major university campus (in this case not larger than 15,000):
Phoenix - ASU-Downtown (6,595)
Dallas - SMU (10,938)
Fort Worth - TCU (9,142)
Nashville - Vanderbilt (12,714)
Oklahoma City - OSU-OKC (5,824)
Colorado Springs - UCCS (9,745)
Omaha - Nebraska-Omaha (14,665)
Tulsa - Tulsa (4,185)
Oakland - Holy Names (1,164)
Wichita - Wichita State (14,577)
New Orleans - New Orleans (11,276)
I closer look might show that your proving our point... concentrating on significant schools:
Phoenix - Arizona State is directly across the river and has 83,000 kids enrolled.
Dallas - as you pointed out, there are several excellent medium sized Universities (TCU & SMU), there is also UT-Dallas with 23k, and U North Texas in Denton with 30+k. And Ft. Worth is metro Dallas.
Nashville - Vanderbilt (13k) as mention, also Tenn State (10k), Bellmont (7.5k), and in the metro area there is also Middle Tennessee State (go Hilltoppers!) with 20k+ kids. as well as U Nashville, Bellmont and Fisk being in town. So what, 60k college kids within 20 miles?
Oklahoma City - In the metro area you also have University of Central Oklahoma with 17k kids, University of Oklahoma with ~ 30k kids, in addition to OCU and other smaller colleges.
Colorado Springs - UCCS, you also have the Air Force Academy! As well as two military bases and the US Olympic training center (which takes a lot away from the need for a
medium city [metro about half of Tulsa metro] to have more than 2 sizable Universities)...but there are also several small (<4k) elite colleges including Colorado Tech.
Omaha - Nebraska-Omaha (14,665) as well as Creighton (8k), and the University of Nebraska is less than 20 miles away.
Oakland - It physically borders UC-Berekely with 39,000 kids, the border of the University is the City limits of Oakland. It is also in a metro area with Stanford, UC San Francisco, US Santa Barbara, City College of San Fran, Cal State, St. Mary's, UC Santa Clara, Cal State East Bay - more than 100k students just at the large state schools within 25 miles of Oakland.
Wichita - Wichita State (14,577), I count that as a major State University. Kansas has 2 flagships, on major, and four minor universities (Pittsburgh, Emporia, Washburm and Ft. Hayes being the minor schools). I'd consider Northern Iowa, Missouri State, etc. to be major universities even though they aren't a flagship school. The MSA is ~400k less than the Tulsa MSA and they have a major State University.
New Orleans - New Orleans (11,276), Tulane (11k), Layola (4.5), Xavier (3.5k)...
Tulsa - Tulsa (4,185), also has Rogers State (4K), NSU (1k), ORU (3.2k), OSU-Tulsa (2.8k), OU-Tulsa (1k)...
Notice a pattern - the cities you listed all have one or two colleges of significant size in their immediate metro as well as small colleges. Tulsa just has a mashup of minor players. If Tulsa had a major university in Sand Springs or Wagner...I don't think we'd be having this discussion. No one in St. Paul is saying they need a new State School because U Minnesota is in Minneapolis. It is equally ridiculously to say OKC doesn't have University with UCO and OU on their borders.