You're just talking camshaft-less poppet valved engine; cam-less engines have been around for ?100 years - Charles Knight patented the sleeve valve in 1908. And by correctly positioning ports on sleeve, one sleeve will provide both intake and exhaust.* But as Ron alludes, it doesn't provide the endless possibilities of camshaft-less design.
In order to start, engine needs air under compression and fuel as vapour (not liquid). Rings don't seal tight enough to maintain compression indefinitely and fuel will condense on cylinder walls/head/piston, so you can't get stopped engine to start without a little assistance. So, you still need a starter motor.

But because you could hold valves open on all but one cylinder, the starter could be much smaller (motorcycle sized).
And you can flow the exhaust from that one cylinder into remaining cylinders, quickly heating them to operating temperature - minimizing cold start emissions (EGR on steroids).
The first challenge is getting rid of the valve springs: Renault's pneumatic valves work fine in racing engines but don't have the longevity to work in consumer automobiles. Until we see pneumatic valves in a production engine, doing the whole camshaft-less is probably too risky for an automotive manufacture. (Until we see a pneumatic valve consumer motorcycle, it still vapourware to me).
The historic problem with camshaft-less poppet valves - the power to run the hydraulic/pneumatic system was enormous (10X the power to run a camshaft). So, while it improved performance and was OK for racing engines where using 10hp to drive valves for 50hp to wheels was acceptable; it wasn't OK for where the 10hp to drive the valves was double the power required to drive the car, so halved fuel economy...
Personally, I am more of a fan of additional power recovery via turbine driving generator (I really like Mercedes F! packaging). Getting more power out of the fuel I put in, beats putting additional fuel in.
*Sleeveless valves scrape carbon away very similar to how it is done with Wankel - similar oil control and thermal issues on exhaust port.