SOHC vs DOHC vs Pushrod Engines: Camshaft Issues
(regarding the advantages of DOHC vs SOHC, or dual-overhead-cam vs single-overhead-cam engines):
DOHC has a major marketing advantage.
With a valve train (camshaft, lifters, pushrods (if present) rockers, valves and springs) there is an advantage to light weight. A valve will be opening 1500 times a minute (25 times a second) at highway cruising speeds (3000 RPM). If the valvetrain weighs a lot, when the camshaft lifts it, it will just keep on going up until the spring finally catches it. That could be a lot of looseness. It's called valve float. You can combat that with stronger (and heavier) springs, but the extra weight compounds the problem and the extra pressure from the stronger spring increases wear and the power needed to open the valve.
A good way to fix this is to lower the weight of the valve train. With a camshaft sitting above the valve, all you have is some sort of lash adjuster (lifter) riding on the cam and the lifter rides on the valve. If all the valves are in line, like on an EEK or even a conventional Detroit V8, one cam will open and close the valves quite well.
But, if you open a 2.2, you'll see that there are actually rockers in there. This adds inertia to the valvetrain, but the payoff here is that the camshaft and its drive sprocket can be a few inches lower, which is good for packaging. It's not like the 2.2/2.5 reach very high engine speeds. A pushrod engine would have been fine, but since it was an all-new engine, they went OHC.
You can actuate four valves per cylinder with one camshaft by using rocker arms to open one set or both, depends on how you want to do it.
As for DOHC, again, there is an advantage in weight, at an extra cost, both financially and in complexity. It costs more to grind two camshafts than one and it takes more stuff to drive two cams than one. Otherwise, it's much like SOHC.
Putting the cam in the block and actuating the valves with pushrods (through rockers) works quite well, too. Until recently, every Detroit V8 did it. So did British Leyland engines in Minis and MGs. Even BMWs in the fifties. The main advantage is that, especially in a V engine, there's only one camshaft. Also, the camshaft drive is a lot shorter which gives better accuracy in timing. Chevrolet is sticking with the pushrod engine because they also tend to be smaller. There's no camshaft up above and no cam sprocket. On a V engine, that makes it both lower and narrower. It also tends to be lighter.
Another reason is that engineers tend to stick with the tried and true. If you look at a flat-head engine, the camshaft is in the same place as it is in a pushrod engine. All they had to do, theoretically, was put a new head with rockers on the flathead engine, as Zora Arkus-Duntov did with the Ardun heads for the Ford flathead V8. You can also use the camshaft as an auxillary drive shaft inside the engine to run the distributer, oil pump and if present, the fuel pump, just like the EEK engines use a countershaft to do this.
There is a big disadvantage with a pushrod engine, and that's valvetrain inertia. Everything else being equal, the valves will float at a lower RPM, but for street driving, even extra-legal street driving, that's not a concern. Roger Penske's car won the Indy 500 a few years ago with a pushrod engine, while everybody else had DOHC.
You can have four valves per cylinder with a pushrod (cam in block) engine, you just have to get fancy with the rockers and pushrods. If you look at a Chrysler Hemi or even a Poly engine, you'll see some pretty fancy pushrodding going on, too.
OHC can be simpler, especially with an inline engine. You just use a longer belt or chain to drive the camshaft and skip the pushrods. On a V engine, you wind up with quite a bit more complexity.
It costs a lot to design and certify a completely new engine. And in the end, it's marketing and cost that drives the design.