Pedaling is one of those things, where there doesn’t seem to be much consensus about. Some piano players advocate a very strict idea about when and how much the pedal should be used, while others think that doing what feels right, what you think is the best way to go. I personally can see both extremes of opinions are valid depending on the context.
In the context of classical music, I think that pedaling should be done exactly as written. This is because the composer who wrote the piece of music put thought into when the pedal should and shouldn’t be used. As classical music is about faithfully reproducing the composer’s work into an authentic rendition of the piece of music, it makes sense that the pedaling should be done as written. I also think that if you could not really be bothered doing this with classical music, then you are better off skipping using the pedal entirely.
There is one exception to this and it is only in a few circumstances. If you are playing a chord that is stretched over more than an octave and that the notes of the chord are meant to be played all at the same time and your hand is not physically big enough to stretch that far, then it is considered reasonable to briefly use the pedal. The way you do this is that your hand plays the notes of the chord as rapidly as possible while pressing on the pedal and it will help in achieving an effect of all the notes played together.
When it comes to playing modern popular music, then I think it is very much the case that you can do what you feel like. If you think a small section would sound better with the pedal then use the pedal. When it comes to modern music, you are not likely to get print music that the composer or composers wrote. What you are getting is a third party’s interpretation of that piece of music. So feel free to make up your own mind.
I do not play jazz piano but from what I have seen and know is that jazz music is more about a personal interpretation of a piece of music, unlike classical music which is about a faithful reproduction of a piece of music. So considering jazz is about using your own style, then by extension, this would apply to pedaling as well.
Despite my own opinion being based on the genre of music being played, one thing that I think is important to all genres is that there is such a thing as over using the pedal. When the pedal is used to much, the notes just all blur into the one muddy sounding mess. So I am of the opinion that it is better to under utilize the pedal than over utilize the pedal – so much better.
If you would rather skip learning to use the pedal at all, unless you are doing piano exams, feel free to skip it entirely, especially if you don’t have the flexibility to move your foot up and down, or that action causes pain or discomfort.