I did it on a Brand new Gen4 G19 at the same time I installed a 3.5 connector. Obviously, I didn't know which made the difference, or was it both. So, I polished my stock connector and reinstalled it and noticed no significant difference compared to complete stock.
The thing I noticed that helped more than anything with my G19 was: when I VERY carefully removed the rough edges at the very rear or top edge of the cruciform. I could feel my trigger hanging up and dragging somewhere right at the very very end, just before it fired. By smoothing out that edge, it allowed the cruciform to smoothly drop down below the firing pin much more smoothly with no hanging or dragging. I was very careful not to remove the main material of it. I ONLY removed the roughness that was left over from when the part was stamped. They may not all be as rough as mine was, I don't know. It was, however, very evident what was causing the dragging, or gritty feel. I took it apart and investigated all parts, when I saw that roughness, I knew that had to be the culprit. If you do this, do it at your own risk. I also took the time to test this gun afterwards in different real time settings to make sure it did not affect safety. I am satisfied that it made my trigger smoother and in no way compromised the safety of the firearm. Disclaimer: results may vary.
I also polished everything on a used Gen3 G30SF that had a pretty sweet trigger when I got it. You could see where everything was "worn in" nicely just from shooting. I decided to polish everything anyhow and noticed zero improvements, not that it needed any.
In summary: I think polishing does very little. I think a lighter connector that is tuned properly will make the biggest improvements. MikeP informed me of the importance of tuning with paper. It made all the difference. Even the connectors that say "drop in" still need to be paper tuned. You can drop in a 3.5 connector and if you don't take the time to adjust it with the paper, it will make no difference and maybe even be worse.
I will also add that if you polish with Flitz or Mothers applied to a Q-tip, you are spinning your wheels. It needs to be done with a Dremel with a buffer attachment. Sure, you are making it shiny with a Q-tip but you are not really smoothing it. I know this because I viewed the same video you referenced and did that before I used a Dremel.
I am now completely satisfied with my G19 trigger. I believe it was a combination of the removing of the roughness on the cruciform and the 3.5 connector that has been properly tuned with paper.