I also think part of the issue is the amount of dice rolling we do for expediency.
For example, lets say I was to play a game of chess with a grand master (and I am not great at chess). The chance to beat them is probably less than 1%, I could easily believe I could play them for a month and never win.
Now one DM might say "ok both of you make an opposed 'chess' roll". And under that condition, the unskilled player will win way more often than is realistic.
Another one may go "give me your passive 10 + 'chess modifier' vs the grand master's". Under such a scenario, I would never beat the grand master.
And a third may go "roll an opposed chess roll for every round of chess". If you win a round, you get a point. If you lose a round, you lose a point. First player to 10 wins. In this scenario, I would have a very small but possible chance to beat the grand master.
The third option is the most realistic. It provides a very small but possible chance of beating someone that has incredible mastery of a thing compared to me...but its also very tedious.
So to me the trick is how you want your "world" to handle this, versus the "PCs". For your world, it probably makes plenty of sense for people to take 10s on almost all things. This means Grand Masters never lose to base pupils at chess. But Pcs always get a straight up roll, because they are "special". So when a PC beats the grand master "that one special time", its a notable thing.