As vitovito mentions, wideband data in high resolution is incredibly expensive from a storage perspective. There are entities that do it, but this also has the same privacy concerns as saving every packet that comes over a wire - in fact if you record 2.4 MHz and 5 MHz you will be picking up someone's (hopefully encrypted) private data. I don't think it is illegal, but the technical aspects of this are pretty daunting.

You would be better off decoding and storing that, but that gets into v& territory pretty quickly, depending on who and what you decode (definitely don't decrypt/crack).