How much does a (for example) system designer have to worry about the efficiency of the logic of their system? Like making sure it's not doing a couple hundred "if" checks every frame, or optimizing path finding.
As a general rule, in any sufficiently large project any script or logic that any designer writes should go through the normal script and code review process. This generally requires engineers and other designers to review the logic and performance of the code, any potential issues or bugs, and make sure that the changes are made according to the coding standard. This provides a first line of defense against bugs and mistakes. Any proposed change would need approval from other engineers/designers. The system designer must fix any problems and make reasonable changes requested by the reviewers before approval is obtained. The code (and design) review process exists to reduce the overall bugs and problems in the depot.
Even in smaller projects, code and script reviews exist because they must. The code review is the first line of defense against bad performance, bugs, and issues. In the small teams I worked with (~20 people or fewer), there was still the expectation of getting another designer or engineer to look over my work before submission to understand what I was doing and point out any issues they saw.
What this means as an answer to your question is "a designer should go through the review process and listen to the expertise from other designers and engineers about how to complete the tasks she's trying to do". Basically, it's up to each designer to listen to the feedback given in the review process and address those issues appropriately before submitting so that the team can collectively prevent as many bugs and issues as they can.
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