Hmmmm.... Okay. Hmmm... (Thinking: chin on hand, brow creased. Thoughtful expression.)
I fly out of a tower airport, but it's not so large that controllers won't learn most of the aircraft well, as well as pilot capabilities. I've enjoyed, several times, a controller calling on me to do something different to relieve congestion or help him aid traffic because he knew I'd understand his instructions and do it well... I enjoy that kind of thing, too.
I agree that calling up needs to be efficient and descriptive. I'm sure I'll go along with whatever they require. But in just thinking and talking, here, processing things, I'm not sure that "Light Sport" as the primary descriptor is informative.
My SportCruiser flies about the same speeds as my Cardinal, and also my Stinson Reliant SR-9B (former), and faster than my old Cessna 120 by quite a bit, and none of them are light sport. Plus some light sports are even slower than my old C-120... I'm gong to make it E-LSA, too, and Experimental seems appropriate, there, too, but some of those will go 300 mph, where some of those will also go quite a bit less than the C-120. (The C-120 does not qualify to be flown LSA because its GW is 1450.

)
In the end, I'm thinking that they'll get used to the plane they know, and some call sign will be recognized as what the plane is. Like: The Stinson. It was an antique TC'd airplane, but we always called it "Gullwing xxxxx," all over the country, as it had this huge gull wing on it (descriptive when they saw it...). Same call sign in Demoines, Dallas, Las Vegas.... A couple times --- DO NOT DO AS I DID!! --- over Los Angeles, a flight following controller asked me "Say type aircraft," and I'd answer specifically "SR-9B." Later on, I'd get say type aircraft again, and I said, "...It's like an old packard Al Capone would have loved to have." I wasn't being difficult. I was reading the controller's interest and was replying with camaraderie, and I got a chuckle for it on the radio. If I thought he was really trying to get me to be literal, I'd have given him that for sure.
But on the home airport, I'm thinking I'll start with "Cruiser xxxxx," as they already know my speed, etc., due to their scope in the tower. If they require "Light sport," I may reply "Light Sport Cruiser," as that's more descriptive. (I speak in an efficient, chopped manner on the radio, so I'm not contributing to frequency congestion, I don't think, overall.)
So we'll see. I've heard it different ways. One, was a preference for the type or model aircraft, as, even if controllers are not familiar with newer designs on thue market, the type or model is more descriptive and specific than the general category "Light sport" or "experimental...," to me...... Aeronca not being light sport, CTLS being notably faster than it is....
(Just my thoughts, enjoying the conversation. In reality, I cooperate with them, do as appropriate/instructed...)
Jen