any reason not to cut it?

Isn't the rim of the filter under the outer ring of the 'lid'? It seems the removing the piece you propose would get you to the inside of the air filter element but not allow you to remove the filter. By the time you get all this cut out is the remaining part of the air cleaner box going to be stiff enough?
yes, it would not allow me to remove the filter

maybe this is a round about way of doing things

I do believe the housing would be sturdy enough