"And he can figure out how to get out of trouble after he learns his magic, how to fly, and what people here think about dragons."

So yes, Strange does spoil Alistair. But he's just a baby! You've got to take care of the baby until they are old enough to go out on their own, isn't that how proper parenting worked? At least, that's how Strange hopes proper parenting works.

"Alistair doesn't like being alone either. Especially at this age, dragonets are social creatures. We can give them all the intellectual development possible, but that doesn't compare to running around and playing with their own kind."