I won't pursue this indefinitely, but many interesting additions have come in on the question of whether Harvard, Yale, etc should/will/must bring back on-campus ROTC programs, now that the main stated objection to the programs is going away. Background here, here, and here; I'll collect all ROTC-related items here.
As a reminder, the programs were originally pushed off-campus in the 1960s in protest of the Vietnam war; through the last two decades, they've been kept out of some elite schools in protest of the military's refusal to accept openly gay service members. Students at those schools can accept ROTC scholarships, but they go off-campus for training -- for instance, to MIT for Harvard students, and to Berkeley (!) for Stanford.
First, from a member of West Point's class of 1972, who says that ROTC's problem is broader than the ban at several campuses and has its own "class war" aspects:
ROTC seems to be disappearing from private universities even where the program survived the Viet Nam era. Around 15 years ago I worked for the North Carolina Army National Guard (NCARNG) in the recruiting office and acted as the coordinator between the NCARNG and the ROTC programs in the state. Davidson College and Duke University both had thriving ROTC programs at that time.
Around this time the Army restructured the ROTC scholarship program to the point where the ROTC scholarship would not cover the costs of attending a private university the way it had before. I saw the ROTC programs at Duke and Davidson shrink from being ROTC battalions to being satellites (the battalions moved to UNC-Chapel Hill and Charlotte, respectively). My contacts at UNC (where I work) and Charlotte (where one of my kids goes and who wants to enroll in ROTC this fall) tell me that this situation still exists. Good people who had the desire to be officers and the academic credentials to go to schools like Duke and Davidson took their ROTC scholarships to state schools where the money went farther. ROTC has been priced out of the market in at least some non-public schools.
Quite frankly, I would accuse the Ivy League schools of contributing to the existing class rift in the country that resulted from the Viet Nam era draft. I would challenge these elite schools to meet the armed forces half way: if the Defense Department does away with DADT, the elite schools need to provide ample scholarship aid to ROTC scholarship cadets to make it feasible to have ROTC back on these campuses...
Now, from a product of Berkeley's ROTC program, who argues that for dollars-and-cents reasons the military will not be rushing to reconstitute programs at Harvard etc even if they are officially welcomed back in:
As a UC Berkeley ROTC graduate and current Naval officer, I feel obliged to point out that there's a fair bit of myth and misinformation surrounding the absence of ROTC units from "elite" campuses. While it's certainly true that many campus administrators and student groups have objected to the presence of ROTC units because of DADT, the services' manning and budgetary demands are what is actually behind the absence of the program at elite universities.
An ROTC program requires an O-6 (Colonel/Captain) to lead the command, and O-5 (Lieutenant Colonel/Commander) to serve as executive officer, and several additional officers and senior enlisted personnel to fill advisory and administrative positions. If a campus's student body is relatively small, an ROTC program will probably not be able to attract a sufficient number of students to justify the expense of maintaining such a staff.
Therefore, ROTC programs are generally found at either campuses with large undergraduate classes, or at schools in close proximity to other universities. For example, the UC Berkeley-hosted Navy ROTC program hosts students from Stanford, UC Davis, and the California Maritime Academy. The MIT-hosted program is made available to students at Harvard and Tufts.
While it's certainly true Stanford and Harvard may choose to lift the ban on ROTC if DADT is repealed, the Navy will almost certainly not invest the resources to begin new programs at either school. Similarly, unless another large university is founded in New Haven, it is doubtful ROTC will come to Yale.
Navy ROTC programs: https://www.nrotc.navy.mil/colleges_nrotc_unitsXP3.aspx
Army ROTC programs: http://branchorientation.com/rotc/find_schools.jsp
Air Force ROTC programs: http://www.afrotc.com/college-life/college-locator/
Finally, after the jump, a Columbia graduate argues that torpor and hidebound-ness on the military's side has made the situation worse.