Usually if you don’t have a working commode you often don’t have a sink or shower either.
That said I’ve seen clothes washers and kitchen sink drain directly onto a lawn with no ill effects. The lawn was thickest where they drained.
Oh and you said “greywater” which infers you are an RVer ?
Greywater is a generic "green" term, though I've done some quasi-RVing. (VW microbus). Draining directly onto the lawn is fine with me: I've seen the same effect as you have.
Some communities in Florida demand that well water used for air conditioning be drained directly onto the ground. (and not injected back down).