FWIW, Stephen Miller, an immigration advisor, has, in the past suggested limiting issuing student visas to "hurt universities whose faculty and students had been critical of Trump" [0]. With this in mind, this motivation becomes more clear and this wouldn't be the first policy from this administration that does collateral damage to their base.
It's like the tax policy change a few years ago to reduce the mortgage interest deduction. This had a much bigger effect on expensive cities and suburbs which are more in Democratic-voting states (CA, NY, CT, NJ, MA, WA, MD, etc). The Republican party lost a few Representatives in those states but it was worth it to them to get the tax bill passed and stick it to the libs.
Look at any county by county map showing who voted for who in a presidential election in the last 20yr. The cities lean left. Where are the universities with graduate programs big enough to attract substantial foreign interest located? Mostly cities. So who gets hurt by this policy the most? Places (and people) who lean left.
Looking at the map of results from the 2016 election in Indiana (where I went to college), the state was solidly pro-Trump but you can easily spot the blue counties where IU Bloomington (Monroe) and Notre Dame (St Joseph) are located. The only other counties where Hillary won are Marion (Indianapolis) and Lake (basically a suburb of Chicago). Tippecanoe county (Purdue Univ) is pink and went for Trump with 49%.
This indicates that even in a "red state", the university towns with lots of international students are already voting left and hurting them with this policy probably wouldn't affect the outcome of the next election.
