It does exist. Car companies have been tinkering with this for over two decades. There exists a military diesel that will run on gasoline. Not well, but it will run.It sounds like something that if it did exist it would already be available for more cars.
The problems are with combustion stability and that means, in the modern world, emissions. It's not an easy problem to solve or it would have been done a long time ago. But physics says it's not impossible -- just hard.
Hybrid tax credits make that path "easier" and less risky -- until they expire. They have expired for some models already -- the main Prius line being one of them. Those tax credits make the consumer think he's getting a good deal, but in fact he's not -- he's buying a pig in a poke, because the long-term operating cost is quite high. If he gets rid of the car before that hits him, so much to the good for him, but not for the next guy.
My '03 Jetta Diesel wagon can return an honest 50mpg on the highway at reasonable speed. It has posted a lifetime average fuel economy of ~43mpg (!) over more than 200,000 miles. I can count on my fingers the number of tanks that it has consumed and returned under 40mpg. However, it can't meet current emissions. The additional crap required to do so is (1) expensive to install, (2) expensive to maintain and (3) introduces additional high-cost failure possibilities that, out-of-warranty, can destroy the economic value of the vehicle. In addition all that crap harms fuel economy enough that the balance no longer makes sense. Thus I refused to buy a "more modern" diesel. But my '03 will out-haul, out-mileage, radically out-perform and outlast a Prius -- it's got over 200k on the clock now with zero failures, requiring only routine maintenance, and STILL gets 50mpg on the highway at reasonable speeds. It lacks (by a lot!) the "6"'s consideration to aerodynamics.
An HCCI-engined "6" will hit that number. It's not THAT far from where I am now; ~37mpg @ 70mph on flat highway; actual full-tank numbers have hit 41mpg @ 63ish mph. 20% efficiency improvement gets me into the mid-40s @70mph. Back off the throttle a bit or get another 5-10% and you're there.
Find me a hybrid 4-door sedan in the same size class that can return 50mpg on the highway. You can't but Mazda is within spitting distance of doing it if HCCI works. The "3", a smaller car, should be able to hit the mid 50s.
Oh, and like all compression-ignition engines there's no mileage penalty from forced induction for additional power (up to the point the engine physically fails due to overstress) unless you use it. This means that Mazda can produce 300hp+ versions of that engine that STILL return 50mpg on the EPA cycle. No, they won't get that kind of economy with a leaded right foot, but you sure as hell will get a big GRIN in exchange for the loss of fuel economy. How do I know? My '03 has materially more power than it did when originally delivered and yet if you don't use it the penalty exacted for that in fuel economy is a literal ZERO, and I didn't go very far because I didn't want to replace the final drive and clutch. Nonetheless the difference from stock in that car when the boost comes on is NOT subtle.