You're talking about a very specific subset of older professors here. One benefit that older PIs have is a lot of grant money and so they can indeed not have to constantly worry about securing funding and providing you with a mentoring opportunity. But here's the problem with this theory. We view undergrads as mentees to be trained in the science and art of research, not scientists who need to publish. This is a common fallacy pre-meds fall into - you join a lab to learn about research and not to publish. Publishing takes a long time and many of us graduate students take two or more years of full-time graduate work to get one first-author paper. Undergrads who work in lab 10-15 hours a week couldn't get a first author paper in a basic science discipline without substantial help. Or if they do, it's low-impact work in a low-impact journal. So my point is, a PI wanting to mentor you is very different than a PI who wants to let you publish. With older PIs, the bar for publication is higher because if you're already well-respected and well-known, you better make sure your work is of the highest quality because there's nowhere left for you to go but down. So in those labs, it's harder for grad students to publish, much less undergrads.
Younger professors will be eager to publish and in their point of view, the more publications, the better. The bar is lower because they need those publications. Also, most of the undergrad mentoring is not done by professors anyway. It's done by us graduate students and post-docs. No matter which lab you're in, your mentoring is dependent on that group of people. The older PIs haven't touched a piece of lab equipment in decades and they're not going to mentor you except an occasional suggestion here and there. Your daily mentoring will be done by the poor grad student or post-doc who has been assigned to you.