Final answer:
Yes, an oil filter should have a bypass valve to ensure oil continues to flow to the engine if the filter is clogged or when cold-starting - it's designed to protect the engine.
Step-by-step explanation:
The question asked if an oil filter should have a bypass valve that oil can flow through when the filter is clogged or during a cold start when the oil is too thick to pass through the filter media.
The answer is yes, an oil filter should have a bypass valve. This is critical because if the filter becomes clogged, the bypass valve will open, allowing oil to continue flowing to the engine, albeit unfiltered, to prevent engine damage from oil starvation. During a cold start, the bypass valve can also serve a similar function, permitting thick oil to bypass the filter media to ensure the engine receives immediate lubrication, which is better than receiving no oil at all. The goal is to protect the engine at all times, even if it means the oil isn't being filtered for a short period.