I am biased, so understand that as you read on.
My son's Ivy had three MLB pitchers and one hitter this year. My son was drafted out of HS and again as a budget single digit round senior. He is out of baseball now and really enjoying his real world career (his first 2 week paycheck was more then he made in any MILB season - which btw, is what you earn for the year).
There are, IMO, 9 d1 schools where the degree the baseball player brings to the job market is viewed the same way as every other typical student from that same school. Those schools are Stanford and the 8 Ivies. That doesn't mean that you cannot do it at other schools, but think of your son as in the middle of the pack, not an outlier and then look where the middle of the pack ends up. I know athletes and non-athletes who graduated from Northwestern, UCLA, USC, Vandy); the job market (especially in anything connected to banking , financing) is easier for the 9 schools.
The middle of the pack at those 9 schools (I am speaking of d1 only) has a dream job waiting for them whenever they decide to enter the workforce. and also realize that even at those schools most of the players graduated with a different major then they matriculated. For some reason most players did change from engineering to economics - which makes Fenways' son so remarkable - but an economics degree from say Yale has big big value in getting the first real world job (beyond that it's up to them)
I have the view that a pro prospect who doesn't blossom as a freshman (the least important year ironically) stands a better chance at an Ivy. Why? Rosters are smaller, so guys get way more chances. Winning isn't a true pressure (although a coach must be Ivy competitive) on the coach. Fewer guys go to summer leagues because most of your teammates are working internships on wallstreet or wherever; but all guys who are legit prospects play where they want (i.e., cape, Northwoods,etc). It's easier to be an all-round developing student/athlete at an Ivy.
Conversely, the pressure on a scholarship guy to perform as a freshman is way more intense outside the Ivy; and (again, IMO) there is a lot going on in the lives of these young men. I'd like to give their athletic talent time to delelop but let's just admit, they are learning to drink, fend off drugs, meeting new people, getting buried in the classroom, working a full time job etc. In the big time baseball conferences, for the coaches it's all about winning. A tough combination for a kid growing into adulthood.
Not only is getting drafted hard enough, succeeding is even harder. I believe hedging the bet of a17-year old is warranted. In another thread, the transfer rate of baseball players was fleshed out; some where like 1/3. I followed my son's roster for 7 years; his team lost two seniors (who graduated on time) and one freshman (mh issues). Moreover, everyone graduated on time except those who were drafted as juniors - both graduated in 6 years.
Roughly 56 players are recruited each year; if you draw the lucky straw there is no need to trade it for what's behind door number 2 (except Stanford).