I have met people who got half way through their undergrad years and then were no longer able to qualify for new loans, and therefore had to drop out. Fortunately they were able to attend a far less expensive state school and graduate from there, but they could have just gone to their state school in the first place and would have ended up with the same degree a year earlier with much less debt.
When I was a graduate student at a very selective top ranked university, there were students who had done their undergrad all over the place. There were many students, possibly a majority, who had done their undergrad at their in-state public flagship. Two things they had in common: They had done very well where ever they were as undergrads; and they had not run up a large debt for undergrad and therefore could afford to go on to graduate school.
We hire graduates from our in-state public flagship university all the time. They work next to MIT graduates on a day to day basis and no one cares who went to which school.