Paul White has a great article on when computed columns perform poorly:
A major cause of poor performance is a simple failure to use an indexed or persisted computed column value as expected. I have lost count of the number of questions I have had over the years asking why the optimizer would choose a terrible execution plan when an obviously better plan using an indexed or persisted computed column exists.
The precise cause in each case varies, but is almost always either a faulty cost-based decision (because scalars are assigned a low fixed cost); or a failure to match an expanded expression back to a persisted computed column or index.
The match-back failures are especially interesting to me, because they often involve complex interactions with orthogonal engine features. Equally often, the failure to “match back” leaves an expression (rather than a column) in a position in the internal query tree that prevents an important optimization rule from matching. In either case, the outcome is the same: a sub-optimal execution plan.
Definitely read the whole thing if you’re thinking about setting trace flag 176 on.