If your printer relies on DHCP then it has to establish a connection to the router (which itself is trying to recover from the power outage) before it reaches a stable state where its able to print. Similarly, the device needing to print has to determine the potentially new IP address for that particular printer before it can send the print job to it.
A static IP address forgoes all that and the device printing can connect with the printer quicker and with less network traffic.
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