There actually isn't a notable difference between the ground clearance on the two bikes. Look at these two pictures and you'll see what I mean.
Both bikes have seventeen inch wheels and the bottom of the bodywork hits almost the same point, which means the ground clearance is very similar between the two.
Also, the key to increasing cornering clearance regarding the engine is to make the bike narrower at the crankshaft. Think about it. But this hasn't been a practical concern for a long time. The limit on cornering clearance for the last 20 years has been the foot peg assemblies, and that is constrained by ergonomic requirements. I've been in this for almost 30 years and I can't remember a sportbike in the liquid cooled era that would deck the case in cornering.
And there definitely was 600 supersport racing in the late 80's in AMA/CCS and WERA, and it was very big. The CBR600 wasn't developed from a sport-touring bike. The way it looked was just the best way the factories knew how to make a 600 sportbike at the time. The 500GP bikes of that era
had the same kind of bulbous styling as the CBR.
About the question from the OP: That's a good question because on paper the new CBR looks like maybe it should have a lower
cg. The first-gen CBR had a steel frame that weighed a lot more than the aluminum frame on the new bike. The new engine has the cases cast together with the cylinder block, and the head is quite a bit smaller and it weighs less than the head on the old bike. Also, look at the suspension, tires and wheels. The new bike has much wider wheels, larger diameter brake rotors, heavier calipers, inverted forks with larger diameter tubes, which have a lower center of mass than the old style of forks. The new CBR is clearly lighter at the top of the bike, but most of the stuff on the bottom is much larger and probably not much lighter overall, if at all. The new CBR does have the undertail exhaust, but the OEM silencers on new bikes are magnitudes lighter than the lead-packed exhausts on bikes back in the 80's. I guarantee that even if you throw in the new exhaust canister, the weight savings from the new aluminum frame are several pounds greater than the old CBR frame.
I bet that if you calculated the center of gravity for the bikes by themselves, the cg for the new CBR might actually be slightly lower than the old bike. But when you put a rider on them, everyone who's been on both would agree the '09 feels much more top heavy.
I think the answer is how the bikes position your body on them. The new CBR has a seat height that is slightly (0.6") higher, but the big difference is the height of the clip-ons and the relationship between the seat height and the clip-ons. Look at the two pictures above. The clip-ons sit a good two or three inches higher than the seat on the 89 CBR, but they're at the same height on the 09. This means the upper half of your body (which weighs the most) will be pushed towards the front tire, which increases the feeling of having a high center of gravity. The pegs are also higher, which raises the of your legs when your on the bike and that pushes the overall cg higher.
About lower cg being better for handling, you'd think so but it doesn't work that way. Honda built a NR bike in the early 80's that mounted the gas tank under the engine to lower the cg and it was practically unrideable.