What is the reason why Buddhist monks don't work to support themselves? Do the monastic rules prohibit them from working?
I recommend you to read the Kasi Bharadvaja Sutta. Kasi Bharadvaja was a farmer who asked this exact question from the Buddha. Monks dedicate their lives to spiritual development. They do not have time to make money or do agriculture. They do not eat for sport or beautification. They only eat enough to maintain life so that they can work towards Nibbana. Yes, farming does break a precept.

"Should any bhikkhu dig soil or have it dug, it is [an offence of Confession.]"