The impression I have of the Alloytec is that it was unnecessarily complex. Were 3 timing chains really the best way to drive four camshafts? Could gears have been used to replace the primary chain and shorten the lengths of the secondary chains? Could two chains have been used instead of 3? And finally, could a cam drive shaft setup have been used?
I mentioned Audi before, design and implementation were two different things, have a read of this -
https://jalopnik.com/here-s-why-the-v8-audi-s4-is-an-awful-used-car-1676466510
Timing chain and it's associated components are supposed to be a life time parts (life of the engine), but when you cut corners and inadvertently make them a not life time part because you're cheap, then it becomes complex because you actually have to take the thing apart which wasn't really supposed to happen. If you look at the Nissan VQ engine or the Toyota GR engine (pretty much Toyota and Nissan Alloytecs) or heeeaps of the Euro engines, they also have three chains (although their layout and chain routing makes a bit more sense) and haven't heard much about those on the level of the Alloytec (although that doesn't really mean much). IMO I'd reckon that 95-99% of cars with chains that aren't terrible would never have a problem. Last chain I personally heard of that needed to be replaced that wasn't on a Commo was my friends DOHC V6 Vitara, the chain was 20 years old. Mostly you remove that part of the equation if you have a timing belt, but the downside is it only works because you're forced to replace it at intervals.
Manufacturers look to where they can cheap out and save money - e.g. they look for something that costs $1 they don't really need, or can be provided for 50c cheaper with a different material, or they can use a different one that kinda does the same thing but doesn't cost as much etc. Across the production of millions of cars that money ads up and ends up being a big saving on paper, the flipside is that you cheap out on the wrong thing and you end up with the reputation of the Alloytec. Lesson to be learned if you're a manufacturer is that if there's one part not to cheap out on for engine production, it's timing chains and chain guides.
Cam drive would be expensive I reckon, not to mention it would probably be extremely bulky for four cam shafts (even if it only had two "feeder/main" shafts). Not to mention, I think it would be difficult to adapt to use for VVT, particularly with the oil based cam phasers all the manufacturers are using now. There's probably also some reason that nobody that uses that style of drive for oil pumps anymore like they did in the 5L and a bunch of American iron.
I know it's not the style you speak of, but OS Giken did a direct gear drive DOHC head at some point in time for the Nissan L series. Have a look at it and you'll see why it's pretty much non existent in production cars, it takes up a lot of real estate on the front of the engine and adds a lot more moving parts to the equation -
http://www.speedhunters.com/2013/02/engine-porn-os-giken-tc24-b1z/