2008 Infiniti Infinity G37 Premium gas necessary?

If your owners manual say it's necessary, then it's necessary. Different engines are engineered differently and running low octane in an engine that requires high octane can seriously damage the engine.

Contrary to popular belief, higher octane fuel does not produce more power. Stuff is added to the gas to make it harder to ignite, but when it does, it burns just like lower octane gas and produces the same power. The purpose of making it harder to ignite is that allows the manufacturer to DESIGN the engine to produce more power. Mainly that means a higher compression ratio. Racing engines and aircraft engines can be smaller than your car engine but produce a lot more power, ... With trade-offs.

Without getting too technical, compression ratio means how much the air going into each cylinder is squeezed into a smaller space. An average value for a car today is around 8:1 which means each gulp of air going in gets squeezed into 1/8 the size space, then a spark from the spark plug ignites the fuel in that air. When you squeeze the air its temperature goes up a lot.

To side-track for a minute, diesel engines have compression ratios of around 22:1. Squeezing the air that much raises its temperature so extremely high that that's what causes the diesel fuel to ignite by itself. There is no need for a spark plug.

It's that self-ignition from high temperatures that is the concern in your engine. We don't want the fuel to ignite before it gets the spark from the spark plug. Timing is critical to proper performance. The additives that result in the octane rating are what prevents the high temperature from igniting the fuel, (called spark knock), and allows the fuel to ignite relatively easily with a spark. Racing engines can have compression ratios as high as 12:1 and to prevent the fuel from self-igniting too soon they may need octane ratings as high as 120 to 150. Those are so high even a spark plug would be unlikely to get that fuel to ignite in your engine.

So basically, if you don't need a higher octane fuel, using one will not gain anything as far as power or performance. In marginal situations where old and worn spark plugs are a concern you may get more misfires, rough running, lower fuel mileage, and more emissions. If you use a lower octane than specified you are likely to get spark knock. That is due to the fuel self-igniting from high temperature before it is supposed to ignite from a spark. You'll hear that as pinging or a rattling noise. That can accelerate engine wear and in severe cases lead to engine damage. You'll also get lower fuel mileage and lower power due to the fuel igniting too soon when the engine isn't in position to make power from the expanding gases. Also, electronic controls, mainly a knock sensor, will detect that spark knock and cause the Engine Computer to take action to reduce power in an attempt to stop that potentially harmful knocking. The spark knock might not occur in cold weather so you might get away with the lower octane fuel then.

What you might do is try some different grade fuels from different gas stations. Keep in mind that if the tank is half full and you fill it from a new station, that is not an accurate test because you still have half the old stuff in there to dilute the new stuff. I would run the tank almost empty, then fill just a quarter tank from a new station. That way if you run into trouble you don't have to use up a bunch of that gas before you can add something else.

I was also recently informed that different gas stations mix the gasohol in different ways. Ethanol has a very high octane rating. To take advantage of that some refiners use an inferior grade of gas because it costs less to refine and they add fewer things that increase the octane rating, because they know ethanol is going to be added later. Some gas stations start with straight gasoline which is a higher quality and has the correct octane rating, then they mix in the ethanol on-site. That boosts the octane rating but they might sell it as a lower grade fuel because their cost is lowered by adding that ethanol. You may actually be buying a higher octane fuel than what you're paying for. That's why you can have different results with the same octane fuel from different gas stations.

Rather than switching straight to the lowest octane you can find, try a mid-grade or buy half of what is called for and the other half a mid-grade, then see what the results are.

As you were already advised, it WILL do engine harm. It burns much hotter and can burn a hole in the piston or melt the valves.

Something else you may have not considered is there may be some spark knock. When that is detected by the knock sensor, the Engine Computer will retard spark timing in an attempt to prevent that. You may not notice that but it will decrease power and fuel mileage.