Gears are heavy, noisy, much more expensive to machine, require lubrication and require more space.
That said I do appreciate that my V4 Saab has geared cam and balance shaft. The rotating masses make the engine smoother, but then having flywheels at BOTH ends of the crank would......
Timing chains are noisy. The link components are cheap to stamp, but there are too many moving parts (at least 8 per link) and when any one fails or wears the entire set is useless. Chains stretch as they wear out requiring tensioners that also require lubrication and slack adjustment fo rmore moving parts. Short chains (cam in block push-rod engines) have fewer links to fail or stretch, but overhead cam engines require longer chains and have more stretch. The cost of chain replacement is multiples of belt replacement do to the chain due to the oil lubricated chain and tensioner being 'inside' the engine.
Belts are quieter, lighter, cheaper to produce, have no moving parts, can be snaked to drive the cam AND the injector pump AND the water pump, are 'external' by not requiring lubrication.