Because the molds that are in blue cheeses have been selected for over the centuries for their taste while those that land on your Cheddar are a random sample. If you kept each one, tasted it, kept the least offensive and used it to start the next round, then eventually you might come up with your own Blue Cheddar that tasted great.

My understanding is that the green moulds more often contain toxic metabolites, possibly largely because of the very selection that Mike mentions. In most standard cheese preparation facilities the fungal cultures are very carefully propagated, or even cloned from single cells.

I cannot remember encountering any specially bad-tasting  green fungi on cheeses, and I have seen quite a few that I would hesitate to call either green or blue. I certainly will not vouch for the safety or danger of any particular strain.

It is safe to eat mould on some cheeses, such as a blue veined variety like stilton. This is because the mould is introduce during production to give certain tastes, but this is done in controlled environments making sure that only this 'safe' mould grows (e.g. a harmless variety of the penicillium fungus). Where as when mould grows on food after purchase where it cannot be controlled, it could be of many different varieties, some of which can be harmful. Therefore you should not ingest or even sniff mould that has grown on cheese after purchase for fear of harmful toxins or spores entering the body.