There's not enough of a market for a live animal delivery company... Logistically, it would take hundreds of trucks in hundreds of cities, not to mention deals with all the airlines (unless you were buying airplanes, like UPS and FedEx do). Thousands of employees.... All the while trying to keep prices halfway decent so that people use it. Plus, there's no way of knowing that you're getting a live animal to begin with. Someone could claim DOA, and if you were intending to guarantee that, you would have to check the health (and to make sure it was even alive to begin with) prior to taking every package. Plus, by opening the package, it makes you responsible, unless you do it with each shipper, which just adds to the time and logistics of it. The network it takes to make a shipping company amazes me. Imagine setting up a company that can take a package from essentially every major city in the US, getting it to almost any other city in an 18 hour period. Still amazes me. And that's just within the US.
I don't think the current shipping methods are all that bad. Yeah, there are bad drivers that don't ask for a signature, but if they're packed properly, it doesn't matter if something is dropped or upside down for a while... I have shipped well over 1,000 boxes of live animals, many of them leaving in the 110-120 degree heat in Las Vegas during the summer months, and to this day I think I've had less than 10 DOA shipments in all of that. Almost all of them I attribute to the heat of Las Vegas (probably half of the DOA's I have had were stuck in Vegas in the summer months the night I shipped them off, and I knew they'd be DOA before they were delivered). It could be much worse.