video – ProRes 4444 with alpha output file is HUGE, how to compress it with FFMPEG?

I am using FFMPEG to output a .mov file. It needs to be a .mov file with an alpha channel. ProRes 4444 supports this, this is the command I use (this is simplified but does show the high increase of file size):

ffmpeg -y -i vid.mov -c:v prores_ks -profile:v 4444 -c:a pcm_s16le -pix_fmt yuva444p10le vid2.mov

The output file shows what I want, but it is HUGE. I mean from a 10.8 MB .mov file, it creates a 340 MB output file. I tried reducing the file size with using the -crf command, but then I get this warning and the file size is unchanged:

Codec AVOption crf (Select the quality for constant quality mode) has not been used for any stream. The most likely reason is either wrong type (e.g. a video option with no video streams) or that it is a private option of some encoder which was not actually used for any stream.

How to output a .mov file with alpha channel with a smaller file size than the lossless ProRes one?