CRI is defined as how closely a light source matches the spectral emission of a thing glowing at a specific temperature. So, for a light source with a 4000 k color temperature its CRI describes how closely its emission matches that of an object that's been heated to 4000 k.

Because incandescent bulbs emit light by heating a filament by definition they will have 100 CRI and its impossible to get any better than that. But the emission curve of incandescent lights doesn't actually resemble that of sunlight at all (sorry for the reddit link). The sun is much hotter than any incandescent bulb and it's light is filtered by our atmosphere, resulting in a much flatter more gently sloping emission curve vs the incandescent curve which is extremely lopsided towards the red.

As you can see in the above link, there are certain high end LED bulbs that do a much better job replicating noon day sunlight than incandescents. And that flatter emissions profile probably provides better color rendering (in terms of being able to distinguish one color from another) than the incandescent ramp.

Now, whether or not you want your bulbs to look like the noon day sun is another matter. Maybe you don't want to disrupt your sleep schedule and you'd much rather their emissions resemble the sunset or a campfire (though in that case many halogen and high output incandescent lamps don't do a great job either). Or maybe you're trying to treat seasonal depression and extra sunlight is exactly what you want. But in any case I think CRI isn't a very useful unit (another reddit link).