While one size doesn't fit all, unless your HS student is a top pick in the draft, unable to handle college learning, or not on any financial aid (academic, Pell, Hope, athletic, etc.) which makes college attendance unaffordable, a clear understanding of the next four years, and the trade-offs which are made, should convince most parents to urge college first, pro second.
Start with your individual kid; ignore the baseball skill aspect initially and focus on the person he is.
Can he live away from home with only baseball to amuse him? Why? Because he will spend the entire first year in a hot hot climate with other 18 year olds. They play baseball seven days a week beginning at 7:00 and ending at 5:00. Ninety percent of the time they are at the field they are doing nothing - literally nothing (sitting in the stands pretending to watch a game, chasing after occasional foul balls, scratching themselves, telling lies to the other kids). They bus the kids to the field from the hotel - where they live two to a hotel room - and perhaps are within walking distance of a mall for entertainment.
There is no pay unless he's assigned to a Rookie league - and the pay is 1k per month, from which clubbies fees, rent, and SS are deducted. He has to forage for one meal a day - the club provides two- do his laundry, arrange his hair cuts, deal with guys who are tense all the time (tempers get very short with so little diversions), and deal with the feeling that baseball is more like work and less like fun, and homesickness. For you military vets, think of basic training, without weekend leave.
Every day until September is like this. Then fall instructional ball - a probability - beginning in mid-September - and replay the above.
Then the "kid" arrives back in your house October, and you have the pleasure of hosting him 24/7 until ST in March. He's not the HS boy you sent away a mere four months before; he's a professional baseball player. As such, he needs to eat, workout, get baseball lessons, several hours every single day. And he needs to sleep and do his diversions (hunt, video games, fish, golf, whatever). What he doesn't have time for is a job - because he already has one. He really needs to workout. Because the competition to get out of complex ball is tough and he needs to get out of complex ball ASAP. If his game is not advancing every day, you can bet that there are others who are advancing their game.
The family all needs to be on the same page here, because it will appear from many perspectives as if he is doing nothing except his diversions. You need to understand that while he would have worked maybe three hours a day in the college offseason, he now works out closer to five every day - this will be the life of your child/man for the next three years.
Turning now to the baseball skills aspect.
At any moment he could get cut/injured. His US amateur status is over. In all events he will have access to the MLB scholarship fund. This fund pays out, under certain circumstances and with a specified limit, a sum of money - taxable by the way - which once tapped must be drained within a set period of time (not very long actually).
In the draft round OP indicated, the player has a shot of getting out of complex ball in his third pro season (second full). The professional advantage is a full season over a kid going to college. In other words, if you are drafted, it's not going to be in the slot rounds. You are being told you are viewed as a guy whose ceiling is MLB and whose floor is quite unknown; just like a college guy - the difference is your baseball development is pro style v. College style. The draft is populated with guys who went to college so college style doesn't seem a detriment.
I think most pro parents will agree that failure is part of the pro game. It's really what you do when failure occurs which measures the true love a player has for the game. The overwhelming majority of HS players who are considered in the draft have never experienced failure; they view the baseball world from the top of the mountain range they inhabit. The next level of ball - whether college or pro - will bring failure. The question is where is the kid best placed to deal with this inevitable consequence of competing.
I know my kid could not have dealt with the magnitude and frequency of baseball failure - without a corresponding opportunity to experience success in other areas. College gives that opportunity; even with collassal baseball failure, you have a full social life, learning opportunity, etc. You fail in proball, until you train your mind to leave failure in the rear view mirror, you can never escape from the only "yard stick" which matters.
In short, a family's default should be college. Don't look for ways to go pro from HS. just enjoy the ride, the attention, the fruition of all those years of collective dreams -then hopefilly you can enjoy it again in college.
Full disclosure: I did not feel this way - nor believe others - when we dealt with this issue out of HS. Baseball did not evolve they way it was supposed to in college. The college fail safe was a good safety net. But the ride nevertheless has continued.