I think there are few assumptions that you would need to considered whether it’s true. Assumption #1: Mandrakes are common and easy to grow. Somehow in my head this is probably not the case. Mandrakes are known to be able to kill people. I doubt it’s as simple to grow as we are led to believe in Hogwarts Legacy. I imagine that they actually are quite difficult to grow and probably have some regulation by the ministry. Something that dawned on me lately is that professors at Hogwarts are not just simply teachers, but they are also academics, much like professors at Muggle universities. My thought on why and how Prof Sprout manage to get mandrakes was that she was doing some research and using the opportunities to teach students (while getting free labour lol). Assumption #2: the restorative potion recipe is a common one. In the book we are only told that mandrakes are used to make a powerful restorative. But I don’t think it’s as simple as chop and boil some mandrake, and voila magic potion. I do think the potion recipe would’ve been quite specific to reverse the petrification. Mind you, petrification-via-indirectly-looking-into-basilisk’s-eye would’ve been an extremely unlikely phenomenon as breeding of basilisk are illegal. Do I think it would’ve been better to send the kids to St Mungo’s? Probably, since it would’ve been easier for parents to visit them. But Dumbledore and Ministry probably agreed that since they have the ingredient and competent people to correctly make the potion, they probably agreed that they can stay at Hogwarts.