The humble Compute Scalar is one of the least well-understood of the execution plan operators, and usually the last place people look for query performance problems. It often appears in execution plans with a very low (or even zero) cost, which goes some way to explaining why people ignore it.
Some readers will already know that a Compute Scalar can contain a call to a user-defined function, and that any T-SQL function with a BEGIN…END
block in its definition can have truly disastrous consequences for performance (see When is a SQL function not a function? by Rob Farley for details).
This post is not about those sorts of concerns.