The patient’s immune system reactivates and, in most cases, gradually destroys the transplant, which is no longer needed. Life goes back to normal, free from a daily schedule of pills and their risks and expense. ---taken from The NYT
If you did, you would create a list of three things: (1) a daily schedule of pills, (2) their risks, (3) expense. The patient would be free of each of these things: they would be free of expense, in particular. I don't think this is meant.
As it stands, the sentence contains a list of two things: (1) a daily schedule of pills, (2) their risks and expense. Item (2) internally contains another two-item list, with 'their' covering both sub-items. The patient is free of their expense [i.e. the expense of the pills]. There might or might not be other expenses.
That said, few people know how to punctuate lists coherently. (He said, going by sad experience at work.)
It certainly sounds a lot better to me with those two ands, LQZ ~ it's almost like three entirely separate entities: (1) a daily schedule of pills, (2) [a daily schedule of] all the risks associated with taking pills, (3) [a daily schedule of worry about] the expense of taking pills.
It sounds remarkably 'flat' without the two ands.
I hope someone will come along with some kind of grammatical explanation. (I can't think of one)
ewie's interpretation of exactly what is listed is also possible, and I considered it, but I didn't think a daily schedule of risks made enough sense, nor a daily schedule of expense. In this the layering is:
free from a daily schedule of [[pills] and [their [risks and expense]]]
My interpretation would be:
free from [[a daily schedule of pills] and [their [risks and expense]]]