Is that market large enough in America to hit a critical mass?

Like most personal services, it's probably a niche. In a luxury, NYC apartment? Sure. As you note they exist. But most people see grocery delivery as a luxury. In fact, I suspect even lawn mowing and maid services are used by a relatively small proportion of the population. Much less having someone take your car to the shop or the various other myriad errands that are always piling up on my todo board.