Doesn't appear you'll be talking him out of keeping the A/C unit. So as long as y'all are happy with a plate, go for it. Neither the HVAC casing or plate are very attractive so doing it for aesthetics reasons are a toss up, but I'd rather have the option of basic air flow besides rolling down the windows. Can't be weight savings since it's a street car. A few pounds isn't going to make a hill of beans difference there.
There will be times you're going to miss it. Guaranteed. But if you ever sell it, some people will want the option of A/C and heat/defrost and will limit your potential customer base. I know I'd pass on that right now.