Why do fire engines need to be charged by the mains electricity?

Answer 1

Depends.

Engines perform best at operating temperatures, so some professional/commercial vehicles are equipped with block heaters, which saves some wear on the engines whenever they are suddenly started.

In some places, the emergency services operate on a "first responder" principle, which means that the fire services may be sent on a medical emergency as well. In that case, the vehicle may have a refrigerator on board to store perishable medical supplies. And that refrigerator would drain the vehicle batter fairly soon unless it has a mains hookup.

This condition is also known as parasitic draw. Normal vehicles have a parasitic draw of less than .050 of a volt (50 mA). Emergency vehicles have many add on accessories that cause the parasitic draw to increase over the allowable amount.