They care, they don't want to get punched in the face so they try and wait until they either fall on the ice or get so tired they obviously want the ref to step in.

A lot of times refs and linesmen try to keep players from fighting. Once swinging starts, the linesmen step back until the players are tangled up or on the ice. This (1) prevents the linesman from getting hit and (2) it's easier to break up two tired/beaten guys than two adrenaline filled guys. In the mean time, the ref stands back and watches to a deliver appropriate penalties and ejections.

In this older video you can see the linesman trying to seperate guys before the swinging starts while the ref keeps an eye where penalties will go. Then Patrick Roy comes out and the ref tries to keep him out of the action...with no luck.

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