Look, I don't like Hilary. I don't think this plan is anything more than an attempt to get votes. But your particular complaint about what would happen if the plan were carried out strikes me as misguided.
Foreign students who are here to get a degree ALREADY get to stay as long as they are working on a degree. The crunch comes when they graduate. They need to have a job lined up to stay in the country, and so companies have a lot of leverage in hiring and then how they treat them afterwards under the H1B program. The degree is already the argument the companies use to get them the H1B.
This whole dynamic is a large part of why they can be used to undercut salaries for permanent residents and citizens. It also creates unnecessary bad feelings toward the US by folks we should actually prefer to stay here rather than going back to somewhere else and help offshoring efforts. The plan seems to me a good solution to breaking this dynamic and reducing H1B abuse.
The only drawback I see, which does need a careful selection of institutions to minimize, is that some folks are justifiably unemployable despite somehow managing to obtain an advanced degree. We wind up with them as permanent residents and that costs something in public services. It's a drop in the bucket compared to the costs for uneducated illegal immigrants, but it is something. On the whole, I'd consider the tradeoff a good one.