I don't know about the whole "real" vs "toy" air compressor issue, but I can say this: Filling a tire is a *lot* faster with a compressor than with a pump. And those flat (or just low) tires always seem to come when you're nearly (or already) late to something.
I get that, I really do... and side by side I'd rather use my compressor than my bike pump for filling up a completely flat tire. But, having done this a few times recently (my tires apparently weren't sealed on the rim very well), here's my experience: when I discovered the flat tire my bike pump was right there and it took me maybe 3-4 minutes to pump it up. My compressor was tucked into its storage compartment with the tire-filler-attachment in another tool box. I would have had to take out the compressor, plug it in to charge it (noisy!), carry it over to the car, uncoil and plug in the hose, attach the filler nozzle, inflate the tire, and then reverse the processes.
It's great if you have a garage and can permanently set up your compressor so it's just a few feet away at all times, but if your car is parked in a driveway, lot, on-street, or away from work (e.g. at work) then the compressor becomes the least useful of the options. You can carry a bike pump or 'toy' compressor in your car; most people won't ever have a 'real' compressor in their cars, so they ahve to hope that they happen to be parked right next to theirs in their home.
Each has its advantages - and disadvantages.