No athlete goes to a 4-yr D1 college intending to transfer (some limited exceptions for 3/2 programs).
Attending multiple institutions isn't the end of the world - I attended (full time) and accumulated credits from three in completing my undergraduate degree. But, changing schools does mean disruption - you lose friends, academic credits, have to adjust to new academics, practice routines, social activities, find new grocery stores, barber shops, banks, find and adjust to new living arrangements, etc. Just another wrench in the gears of growing up.
Because - as you note - 50% of baseball players transfer, it is clearly doable.
I would hypothesize that playing time (or lack thereof), grades, girl friend issues, finances, coaching change, character issues (e.g., arrest) - in that order - are the overwhelming reasons for transfers. How would you go about predicting these?
Why are you wasting time even thinking about this? Is there some action you would take or not take knowing the transfer rate? Do you have a crystal ball or magic coin to flip to determine which 50% your son is in?
(In many threads, it is noted that there are a few D1 schools with minimal to no transfers; service academies, Ivy, maybe some Patriot league teams. With this info, what changes in your recruiting?)
Baseball skills and academics. That's it. Take care of that and the rest is derivative (e.g., path of exposure).