I think it does happen by itself. After all, normally focusing your mind on a task full time does lead to superior knowledge and capability, and academics/government officials are able to spend all day on whatever their given topic is.

The problem is it's not sufficient to have time and money. You also need to be in an environment where you're expected to deliver genuine truth, and there are rewards for doing so and penalties for not doing so. And in the public/academic sector these things are lacking, which is sufficient to overpower the specialising effect of full time employment.