I suppose it depends on what you mean by significant. I attended a large research university for both undergrad and grad school, and I’d have to say in my experience, it was not the majority of undergraduates who had that experience, but it wasn’t uncommon either. Some of it has to do with the personality of the professor, but even more of it has to do with the particular undergraduate student and how motivated and intelligent they are. I would also say it is relatively uncommon for the undergraduates who work only over the summers and much more common for those that work during the semesters for a given professor as well.
LACs have a certain advantage built in when it comes to getting to know the professors teaching your classes, that much is certainly true. It has always been my opinion based on observation that something similar can be achieved at a large research institution, but the onus is much more on the student to make the effort to get to know a given subset of the professors. I am sure this is less true in the extremely large undergraduate courses like economics 101, but it’s the later courses whose professors can write the most effective letters anyway.
Further, you only need 3 letters anyway, so it isn’t necessarily a disadvantage to miss out on getting to know every professor (I suspect this is highly student-dependent). Also, I would argue that it is at least as useful to have one very good letter of reference based on your research experience with two medium-quality references based on classes as opposed to three good ones from professors who you knew fairly well from courses. In that regard, I think going to a major research institution is at least as good at grooming graduate students as a LAC provided that a student actually takes advantage of the opportunities available at said research school. Most do not.
I think the expectation at most of these programs is that the summer students will come from other students as a sort of recruiting tool for getting graduate students that otherwise would have no direct exposure to the program. It is more expected that undergraduates that currently attend a given institution already have the opportunity to get involved in that research during the semester. In fact, of all the professors I have known, most who hire undergraduate workers are more than happy to keep them on over the summer without having to go through a formal REU program of any sort. It just seems like few of them actually do this, as many of them chase the money inherent in internships.
I will also point out that everything I have expressed here is based on my experiences in STEM fields. I am sure there is considerable variability across fields.
I couldn’t possibly agree with this more. Hopefully that came across in my early-morning ramble above.
While I am not all that familiar with medical schools, I’ve always heard that they also like the STEM fields on account of the particular brand of problem solving those students practice.
All I really know is that I would be awful at medicine.