A fly similar to The House Fly that DOES bite and ingest blood is called the Stable Fly - Stomoxys calcitrans. This nasty critter readily bites, feeding on livestock, dogs, and our ankles if we leave them available. The mouth of the stable fly is a long, sharp beak or proboscis that it plunges into the skin, and it is not necessarily as polite as many other blood feeders are that first numb that area before biting. You generally feel the sharp pain of the bite from this fly. 

While The House Fly maggots are not generally the ones involved, other maggots may be found feeding on human and other animal flesh, and in fact this may be purposely induced and referred to as Maggot Therapy. Blow flies are the ones that most often seek out fresh wounds on mammals, the adults depositing eggs on the wound and the maggots then feeding on the tissues in that area. If all goes well with blow flies the maggots feed only on dead tissues and leave the live stuff alone, and while we may prefer just some band aids and an aspirin there really seems to be a benefit from letting the maggots do their thing. Eating away the dead tissue helps to cleanse that wound, and the writhing and wriggling of the maggots seems to stimulate the healing process. I suppose an open-minded individual could describe the sensation as "ticklish", but there probably are not too many of those individuals out there. 

We also have plenty of other blood-feeding flies around us, the largest being horse flies, next down deer flies, and then much smaller at no-see-ums, black flies, and mosquitoes. Seems as if Nature provided plenty of them and didn't need to toss The House Fly into the mix.