Roll center coincident with center of gravity implies (for any vehicle of somewhat "normal" shape!) an extremely high roll center.
One bad side effect of doing that, is that if that wheel goes over a one-wheel bump, the geometry causes the tire contact patch to kick sideways. At a minimum, that's going to cause some interesting tire wear. If this is for a front suspension, that's going to cause a big, unpleasant, sideways kick in the steering wheel. It's also going to cause a rough ride ("for every action, there is an equal and opposite reaction" - the sideways kick of the tire contact patch will be translated into a sideways kick of the entire bodywhell, too).
If this is an independent suspension, another bad side effect is that the geometry of ANY high-roll-center independent suspension causes an upward jacking effect in response to cornering loads. For an example of this, look at original (air cooled) VW Beetle, original (first design) Chevrolet Corvair, original (rear engine) Fiat 500 and 126, and a variety of other cars from back then. The common design element is a swing-axle rear suspension design which inherently has a very high roll center. There is a video out there on Youtube of a Fiat 126 cornering, the rear end visibly jacking itself up, and the car basically "tripping" over its own axles and rolling over.
All of these suspension designs are now regarded as obsolete. All modern independent suspensions have much lower roll centers.
You can get away with a higher roll center on a beam-axle suspension, but it still has a bad effect on the ride quality if the roll center is too high. The sideways-kicking over one-wheel bumps is still there.
Compare the ride qualities of a Fox-body Ford Mustang to the current model if you want an example - particularly if the owner has gone ahead and put in stiffer suspension bushings, particularly for the upper diagonal links of the "quadralink" a.k.a. "quadrabind" suspension on the Fox-body. The Fox body uses a pair of diagonal links that place the roll center above the differential housing. The new one uses a panhard rod that is roughly at axle height.
You can make a quadralink axle suspension ride decently (it was commonly used on luxury cars back in the day) ... if you use really soft, compliant bushings and tires with soft sidewalls, to compliantly absorb some of the side kick. Handling suffers accordingly.