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It is a common misconception that the power cable and port are loose. The port itself is a little loose by design as it is a replaceable component.
With all new power cables, the base of the cable offers extra resistance at first and sometimes feels like it is pushed in as far as possible. If you make a fist around the port, and use your other hand for extra leverage, you can give a firm push in and the power cable should slide another quarter-inch further in.