Since others here have posted that they don't have any paint issues without the hood liner, I'd say it's probably OK to not have it on the Crossfire. But on other cars I have seen paint issued caused by a lack of a hood liner. In one particular case, the checking in the paint was so bad that the only fix was to repaint the hood. The underside of the hood had a fairly large "X" cross brace and when looking at the paint on the outside of the hood it was quite obvious that there was no checking in the paint over that crossbrace. In this case, the bracing must have provided just enough insulation to prevent the paint from checking. The car? A previous generation Ford Focus. Just a little naturally aspirated 4 banger, bone stock, but it produced enough heat to damage the paint. I've seen it on other cars, too.

I'd be reluctant to remove mine, but since others here claim no issues after removing theirs, it's hard to argue about it on the Crossfire. Not all cars/hoods/engines are created equal.