Why is it easier to climb in regions with smaller playerbases?

Think about it this way.

In a hypothetical situation, you're running in a race against a bunch of randomly selected strangers. Only 5 people can be "winners" in this race. You know that, of these strangers, 5% of them are considered "elite" level runners. These "elite" level runners are better than you, but not by much. If this race has 19 other people, then of the 20 total people only 1 person will be considered "elite" level, which means you have a higher likelihood of being in the top 5. If the size of the competition was increased to 1000 runners, 50 of them would be considered "elite" level, meaning you have a much lower chance of being in the top 5.

The same is true for League of Legends regions.

The Challenger rank in larger regions has a limit of 300 people, and larger population servers represent a larger competition sphere, each player trying to climb higher than you on the ladder. The limit of 300 (an increase from smaller regions' 50/200) is an attempt to be proportional with the region size, but the population difference is great enough that the limit doesn't compensate. With that larger sample size, the chance of randomly matched players being better than you, or of similar skill level (if you're an elite level player,) is far higher.

So, being in the top 2.5% of players, as the Reddit post you linked mentions, is a much more profound achievement in North America than it is in Oceania, because you're considered better than a much larger amount of people.

One last supporting point might be that the larger regions have a much larger amount of professional, or semi-professional, players in the highest skill levels. NA/EU/KR/CN all have large professional scenes, in stark contrast to OCE or JPN's pro scenes. Less professional players in a region means the higher skill distribution playerbase is less inundated with exceptional elites, granting extra space for more casual players to rise to the highest ranks.