The NBA has structure. This isn't 1994. It's not even 2006. The NBA improved the transition process immensely. Ray Allen himself usually speaks at the transition program.
His team will invest in him. The owners these days are pretty much all savvy business people who know they need to invest in their assets. Personal trainers, team nutritionists, and usually personal chefs. Countless strength and training staff. Business and brand training. Social media training. NBA teams are now also required to have mental health staff.
He won't be any significantly less lonely or more ready for the NBA travel schedule if he leaves at age 21 vs. age 20. But he will be graded more harshly and will have to meet much higher standards and benchmarks by NBA front offices. He will have to absolutely dominate college basketball next season. Could he? Sure. But he's already passed those benchmarks this season. There's 0 reason to risk it.
Additionally, the money for the 30th pick has doubled since 2006. Bouk will make a minimum of $8.2 million and more likely in the $13-18 million (pick #15 or #8) for his first 4 years. The money is literally too good to pass up.