@Mom2aphysicsgeek, yes, thanks for clarifying that about the 3+2. In addition to all the reasons you cite as to why it isn’t the best choice for a lot of students, I have yet to meet or read of ANYONE who went that route. I’m sure they’re out there, but they’re kind of like unicorns. 
Theoretically, they’re intended for the student who wants to receive a true liberal arts education BEFORE settling into engineering (thus, the fifth year), not so much the math/science-focused student, but they’re mainly used as a marketing tool in my experience.
The 4+1 with UPenn that Haverford and Bryn Mawr offer (and maybe others at this point) is four years for a BS in physics or math typically, plus one year for a master’s in engineering. While Haverford and Bryn Mawr (and Penn for undergrad) offer need-based aid, when we investigated the program at the start of its first year, it was made clear to us that no FA was available for that fifth year at Penn. That’s a VERY expensive year.
@SculptorDad, thanks for clarifying. I think the one thing that separates engineering from business (or whatever) is that, assuming it’s ABET-accredited, there really are no “barely accredited universities” with ABET-accredited engineering programs. There are 150 colleges and universities in the US with ABET-accredited chemical engineering programs. Granted, there’s no doubt a big gap between MIT, Caltech & GT and several of the smaller colleges offering the degree, but, in general, if it’s a large public uni with an ABET-accredited program, you should be fine.
https://www.aiche.org/community/students/abet-accredited-universities
Obviously, if money is not an issue, go to the school that offers the most prestige (or whatever floats your boat), but one of the upsides with an ABET-accredited engineering degree is that, due to the uniform rigor of the degree program, you can get a fine (and sometimes better) education at a more affordable public school.