These are good questions. 18 volts with 250 watts is 13.89 amps but you've calculated for a total input power of 250 watts. The maximum theoretical output would be when the collector dissipation itself has reached 250 watts. The input power required to do that will depend on the amplifiers efficiency. You also make a valid point I overlooked. At 18 volts it will not be possible to reach the maximum collector dissipation before you exceed the maximum current. However, with class C you don't need to come close to the maximum dissipation to make 250 watts output.
I have to admit I have learned some things from this tread also
I thought the 2SC2879 was rated at 20 amps maximum collector current for the last 20 years. It's actually rated at 25 amps. Which explains why the 20 amps fuses in my protection circuit worked best at preventing transistor failure. It takes a few extra amps before that fuse is going to heat up and melt. Back then I didn't even have an amp meter that could read higher then 10 amps DC.