To me it seems like a sort of weird scenario that you would nest programs, and in general you really can't do it. I've never been in a situation where I wanted to create an email program within a parent Default program, for example. And the only other case where you can quasi-nest a program is using one within an Engagement Program step. For the most part I would suggest just using folders on your top level and to separate programs and assets, and keep your programs separate - better for reporting, campaign membership etc. that way anyway, imho.
Would love to hear feedback from others whether there are other use cases for this though!