A few things. First, engineering requires a lot of hours. The room for a large variety of general education courses is limited. It can help if he has a lot of credits coming in but many of the math and science courses will either not be usable or he should consider carefully concerning retaking. My D used her credits primarily for her gen eds and was able to reduce the average number of hours as an engineering student to an average of 15 - 16. Some of those included research. I mention this because if he stays with engineering he probably won’t have time to be taking a lot of non engineering courses. The advantage of being at a school that is larger and is strong in a variety of fields is if he chooses to change his major he will have more and different options.
Second, I can appreciate his desire for a name brand school but it really does eliminate some very good engineering schools. Schools that people in Ohio might recognize as very good schools for Engineering people in other states will never have heard of. Many of them would be considered safeties for your son. U of Cincinnati, U of Toledo, University of Dayton, University of Akron (especially for Chemical Engineering) and even Ohio University are all very good engineering schools with great outcomes for engaged students. U of C and U of Toledo have mandatory coops. I’m sure it’s the same in most parts of the country. There are probably schools that have great engineering programs that we never considered simply because they weren’t near us.
Finally, the question of first year engineering programs and cutoffs. Nearly all first year engineers will take similar courses regardless if they have a direct enrollment into a specific engineering major or not. Most students have little idea what is involved in the various engineering majors they can choose. The courses they take freshman year will give them a taste of the rigor of their engineering path and typically at least one course will educate them on what the various engineering disciplines entail. Once a path is chosen it’s fairly sequential and can be difficult to change. Giving students a year to understand what they will be studying I don’t think is a bad idea. Many HS students won’t be ready to make that decision. There are a number that think because they like Chemistry they should consider Chemical Engineering. What they won’t know is that it requires far more physics than chemistry and they won’t necessarily be the same course a mechanical or civil engineer would take. All schools have to consider class size. The other way to do this is to become much more particular about who you admit. There are pros and cons to each method.