"Persisted" column is not used
The most likely answer to your question lies in this blog post from Paul White: Properly Persisted Computed Columns

The lack of optimizer cost model support means SQL Server assigns a small fixed cost to scalar computations, regardless of complexity or implementation. As a consequence, the server often decides to recompute a stored computed column value instead of reading the persisted or indexed value directly. This is particularly painful when the computed expression is expensive, for example when it involves calling a scalar user-defined function.

It sounds very much like SQL Server has decided that it would rather recompute the column value rather than read it from disk.
One solution, as mentioned by Paul, is to use trace flag 176 to disable computed column expansion.