There are some with good color rendering (CRI over 95 - 98), but they are hard to find and much more expensive than the average LED light bulb (many doesn't even have their CRI specified so probably below 70).

AFAIK None of them will ever have continuous spectrum (like the sun or incandescent bulbs), that's a limitation of the physics how they make light.

Never quite understood the color spectrum complaint, most of the incandescent bulbs I've ever seen are astoundingly red (low temperature), while I've always gotten the greatest color accuracy in my spaces from daylight-temp LEDs.