If I understand it, gearing only changes the speed of rotation, not the power.
There is a problem with terminology. You can increase torque with gearing but you can not increase power. No matter what you do, you can't get more "power" out than you put in.
Metal removal often has a sweet spot where DOC, Feed and SF/M all combine for the particular tooling you are using. Sharp tools cut freer but dull quicker. My carbide inserts, that are for aluminum, cut steel beautifully but dull relatively fast. The nicest thing about them is being able to take a very fine cut in steel much like my HSS tooling. I can even sharpen the "for aluminum" carbide inserts a couple of times on the tool & cutter grinder.
Just play with the variables until you find what works best for you.
I've tested to see how much material I could take off in a given time. Pretty amazing actually.
The snip you quoted removed important context. You are correct in the technical sense. Electrical power cannot be increased. The power delivered; i.e., torque, can definitely be multiplied by gearing. The net result is the same; the workpiece has more force turning it.
Guys, the definition of power is "work performed over time." Watts are joules per second, for example. Torque, on the other hand, is force applied at a distance from the center of a rotating mass, as in pounds-feet or inch-pounds, without reference to time. Torque can be entirely static, as when we are just finished tightening a bolt. Gearing increases torque, but slows down the rotation, so the force is higher but the speed is lower, resulting in the same power.
Torque is what pushes a tool through a material on a lathe, but power is what dictates how fast we can do that pushing. A given volume of material removal will take the same power (assuming constant efficiency, which is an unrealistic assumption that would also have to take tool geometry and material into account) whether or not we use a shallow depth of cut at high speed or a deep cut at low speed.
Lathes that slow the speed electrically rather than using gearing will not see the torque multiplication because the motor itself will produce less power when slowed down that way. That undermines the reciprocal relationship (again, assuming constant efficiency) between force and time.
I had learned this in physics, but it really came home to me when comparing engine torque and power ratings. Many high-power engines have to turn 8000 RPM to get that high power, while many high-torque engines have low horsepower rating simply because they can't turn fast enough to generate high power ratings. A diesel truck engine may produce a 1000 ft-pounds of torque but may do it at 1200 RPM and red-line at 2000 RPM. H=T x RPM/5252, so that engine will produce 380 HP at 2000 RPM. A car engine that produces 380 HP at 6000 RPM may only produce 330 ft-lbs of torque at some much lower RPM, maybe in the 3000-3600 range. Both will take the same amount of time to do the same amount of work. (Again, assuming constant efficiency, plus trucks are, of course, much heavier than cars, so "the same amount of work" takes some effort to imagine.)
The notion of speeds and feeds are a consideration of the efficiency of the tool and material combination. The charts suggest what speeds and feeds will produce the highest tool-cutting efficiency, but that may not be the highest efficiency of the lathe. Those charts assume the lathe has abundant power to handle the suggested speeds and feeds.
Rick "Archimedes" Denney