ffv1 realtime capture throws out a lot of frame dropped messages!
I get the same result with your commands, however if I skip the pixel format conversion and use the input pixel format 'bgr0', then except for an initial frame drop, I get no further drops. Note that tune is a x264 parameter - it has no relevance for FFV1.

And if I use gdigrab (my preferred grabbing device), I get no frame drops at all, even with bgra:-

ffmpeg -y -f gdigrab -i desktop -framerate 30 -c:v ffv1 -pix_fmt bgra -t 5 capture.mkv