Yes, MR, you have nailed the essence of it: Bottom line, lots to play with.
Starter torque(&power) is related to the starter, the amps, which makes it dependent upon the battery, battery cables, and connections.
Engine speed is related to the starter speed (as a result of the torque), the viscosity of the hydraulic oil, and the viscosity of the engine oil, both of which is dependent on temperature.
Ignition is dependent on coil voltage and current (i.e. power) which is dependent on spark plug gap, and cleanliness, and ignition wire integrity and connections, engine speed, which drives compression, which drives temperature, which warms the spark plug which reduces resistance to ignition...
Oh yeah, and all of that fuel/air stuff including mixing, and air temperature that are necessary to actually ignite.
I'm always amazed that engines run. Or maybe that my engines run.
Now all one has to do is decide what you want to spend money on...
I've certainly "fixed" a few engines by using better coils and ignition systems, even without changing wires. I've had other ones that were very, very particular on the ignition wire quality for smooth running, and ones that basically required a lighter to preheat the spark plugs to get the car to start. YMMV.
I can't believe the snow in the northeast;
What Record-Breaking Snow Really Looks Like - The Atlantic
All the best,
Peter