As I’ve read, alternative starting systems nowadays used mostly in commercial, industrial and emergency applications, where it is mission-critical to get it started, such as back-up power generator in the hospital, fire pump on an oil rig, or a life boat. Redundancy is required in some of these situations; in others there is no other option even. There are commercial lorries, mining, quarry and construction vehicles, or generators in remote areas where the only system to start an engine would be the air (pneumatic) or hydraulic start. It is a lot easier to find compressed air than to find reliable electricity to charge a battery in some underdeveloped countries.
Most of those are, of course, are powered by Diesel engines, and do not even need electricity to operate, so some of the vehicles or machines would not even have a battery at all. And, by the way, there are, as I’ve read, hand crank systems on some of those: it is possible to use compression-release mechanism to make it easy to spin the engine by hand to get the flywheel going, then dis-engage CR, and kinetic energy stored in the flywheel should be enough to get it started.
On the other side of the spectrum would be open-wheel race cars (Formulas, Indy, possibly others, such as Le Mans or GT) that do not even have on-board starting system and need to have an external air- or electric start device to get going. Obviously, this is done to save weight — this way they do not need relatively heavy starter motor, and they can get away with much smaller battery which is used more as a current stabilizer rather than storage.
As for regular automobiles, there are several factors that prevent manufacturers from using redundant starting systems:
First of all, regular electric start is pretty reliable. All of us experience dead battery now and again, but mostly due to our own negligence. And in between, there are hundreds, if not thousands, starts the system handles without mechanical failure of the starter motor or natural degradation of the battery.
Secondly, although it is not high-performance racing application, the considerations of weight and cost still play an important role.
Modern cars use internal space rather efficiently, and there simply not many options to put another component, and have an easy access to it.
There are after-market systems allowing for that extra reliability for bigger utility vehicles like pick-ups for farmers or loggers and the like, but then again, that qualifies it as industrial application, because no one but Americans use those for getting to the office or snatching some milk in a neighbourhood shop.