Because the filter will catch more than the screen on the C6 did. There just isn't enough junk in a transmission to plug up a filter until the trans fails. Then the filter needs to be changed.
If you prefer changing the filter, go ahead. I don't think it helps enough to make it worthwhile, but it won't hurt, either.
It should be running about 170-180°F. That's WAY too hot for normal driving. Something is wrong. Your bypass could be stuck open, which will eliminate flow to the coolers. Or you could have a restricted cooler circuit which will open the bypass. Or your coolers could have bugs/leaves/paper/etc covering them.
You are safe to run to 250°F for no more than a half hour at a time. Longer than that you might have problems. I recommend stopping and idling or fast idling in park or neutral if the temp gets to 260°F. Don't shut it off hot, that will cook the transmission.