Generator harmonics question(s)

Years ago I adjusted a neighbor's generator so that it put out 60 cycles at 120 volts. I used a TEK 465B 'scope to look at the frequency. I saw the major 60 cycle waveform and then a lot of smaller waveforms at higher frequencies. I was told that these harmonics were typical of small generators. Today I am replacing the voltage regulator on a small generator and adjusting the governor. I expect I will see the same thing as with my neighbor's generator. Looking inside the generator all I see is rotating coils inside a stationary coil. The rotating coils are energized with DC from the voltage regulator. Looking at old power plant pictures and video it looks as if those giant generators were built the same way. And many of them are still in use today. But I know that the sine wave from the wall has been very good for almost since, if not since, the first generator installation at Niagara Falls. So how do they get the good clean AC from these big generators? Or maybe it's not so clean and is instead filtered. If so how is this done? And can I do this myself without too much effort? Is the effort even worth it? Until the voltage regulator failed on my generator it ran my stuff at home just fine. The fridge, freezer, lights, phone and router. I didn't try any computers. So maybe I don't need to even consider filtering the generator output. But I do see a lot of generators that advertise "pure sine wave output" from an inverter that is part of the generator electronics. So maybe a pure sine wave is important for some electric or electronic stuff. Clocks for example. Anyway, thanks for reading. And for any answers too. Cheers, Eric