Are you sure you're not looking at SPDs for CFLs instead?
LED lightbulbs at least typically seem to have relatively broad and even spectral coverage, even if the distribution is a little lumpy and only a rough approximation of a BB.
All the SPDs of CFLs I've seen on other other hand, are vastly worse, with lots of super intense and narrow spikes in the middle of large areas of almost nothing.
In other words, CFL SPDs look nothing like a BB SPD, whereas LEDs can kinda-sorta-come-close-if-you-squint (it depends on the particular bulb, but some are not bad at all).
[LED lighting also seems much more likely to improve significantly in the future, as it's been developed for a much shorter time than florescent lighting.]
I'm not running a lab or anything where CRI is critical. I had simply preferred high-CRI when I was given the luxury of opting for that when I switched my house from incandescent to fluorescent ten years ago. I would like to see better CRI in LED, but to-date it doesn't seem to be a focus, even amount the high-end brands.