“but storing ALL speech on phones would big a huge undertaking”
Not really.
Voice uses far fewer bits and bandwidth than data.
A modern VoIP conversation only takes 8kbs. A short email is about 100kbytes...and very short at that.
Voice is the EASY and CHEAP stuff.
They probably wash everything in real time looking for words or phrases that throw flags. Then that call may be recorded, and of course certain individuals and groups are targeted.