Query tuning to meet timeout settings
Is this a normal/common approach to solving this kind of problem?


Yes it is a common approach (though not common enough, perhaps).


  Why do I have to help out the optimizer in this way?


Primarily because the optimizer is cost-based, and relies on cardinality estimations (expected number of rows) as a main input to that calculation.

Assuming the right statistics are available, and they are reasonably up-to-date, estimates on base relations may be quite accurate. These derived estimates are the input to the next operation (for example, a join), which produces another cardinality estimation as its output, and so on. The nature of this process (and the statistical inputs) means that the accuracy of the estimations will tend to degrade as derivations continue up the tree. Poor estimations lead to poor cost-based choices, and other side-effects such as an insufficient memory reservation for a hashing or sorting operation.

Materializing intermediate results (using temporary tables, or another method) gives the optimizer a new starting point, perhaps with new statistics automatically built on the materialized data, and maybe even with helpful indexes. These considerations mean that simpler queries (using operations with accurate estimation logic) tend to produce higher-quality execution plans.