Pretty sure those different radio stacks do not run very well in parallel or if they do, they'd likely start to starve the rest in terms of resources needed.
The nRF52840 is not the most performant, I would've really liked if they had chosen a SoC, like the nRF5340, with more RAM or cores for this reason amongst others.
There are similar devices (i.e. SiLabs) that allow multi-protocol use with the radio (I would expect Nordic to have a similar feature set), tho yes, you're right the resource issue would be a major limitation.
The nRF52840 is not the most performant, I would've really liked if they had chosen a SoC, like the nRF5340, with more RAM or cores for this reason amongst others.