Do you live in the countryside? If not, you cannot speak on the subject of bad ping to even a slight extent. People in the countryside not only get tremendously slower upload and download speeds, but also get throttled if: more than one person in your household is utilizing the internet at once (aside from basic tasks like emails), it is during peak hours where many in the neighborhood have gotten off of work and they too want to enjoy the internet (typically 5-9 P.M. on weekdays, weekends are unpredictable), or if anything beyond light rain is occurring.
Also, do you live alone? Do you live with people who use the internet heavily and/or frequently?
I understand your sentiment honestly; some people are lazy fucks and should seriously get an ethernet cable. But if you live in the countryside, your ping will be horrendously unpredictable and uncontrolled, and there is no workaround outside of moving.
And no, it does matter what mode it is. You want to play competitively, go play ranked. Normals, though certainly is not designed for fucking around, also is not even remotely meant to be played by people who want to tryhard. I don't care what you're trying to prove, nor do I care about your "Lee Sin plays"; ranked is for you to play with that attitude.