Rate of character advancement is definitely linked into the power levels, the number of people at those respective power levels, and what needs to be done to get between one level and another. This isn't a discussion for people who want iron-clad definitions of game balance, the very nature of having one character more powerful than another brings asymmetry to the table. It's also important to consider that power may be defined according to a few different metrics.
In super hero games it's often easy to see discrepancy in power levels. One character has awesome special powers (he is a virtual god with a "magic" hammer), another has a special knack that gives them an advantage if they're in the right situation (she can talk to squirrels), while others are just the regular rank and file that makes up the wider world. Such powers are often pretty static, but characters are able to develop the selves in other ways. All other things being equal, the awesome powered character might always beat the minor powered one, but if the lower powered character has social capital in the form of allies, reputation, or personality, they might be able to turn the tables. The powers remain the same, but the characters still have the chance of developing in other areas.
In other settings, similar things might apply. Maybe the physical stats remain the same (or even degrade over time), while mental stats improve and influence throughout the world expands. That might be a fun concept for a game revolving around Knights or Samurai at the twilight of their career on the battlefield.
What I'm thinking about more specifically though is the start of a character's story...not backstory, the point where we meet them and where we move forward. I like heroic tales, so I start the characters somewhere near the middle and hope to watch them ascend to confront the figures at the top. But how long does this take? If it only takes a single session/adventure to get from middle of the pack to the higher levels, then why don't everyone end up at this level? Maybe a simple answer is that stories and adventures capable of bringing such transcendence are very rare phenomena. It probably makes more sense that these events are a bit more common, but regular folk have an aversion to adventure (as we see among the Hobbits of the shire in Tolkein's work...and has basically become a trope of it's own). Under this idea, adventures are there for the taking, and you might gain enlightenment/power through their pursuit, but you have to sacrifice something for that chance. This is basically where the heroes journey fits, so many of us know the routine.
Another route to take is the L5R/caste system route. If you're telling stories of honour, a character might never ascend from one level to the next, but a great deed might see the next generation begin with higher status than the last. In tales like this, it could be very frustrating to play an entire campaign where nothing changes but the hope that a new campaign will see a possible improvement in station. Some people like these "slice of life" simulations of existence in other worlds, I find them a bit tedious.
In the live game I'm currently a part of, I've played a number of sessions where I haven't seen any improvement in my character. Everything works of training through accumulated gold, and I needed 1000 gold to pick up a new ability. Each game you gain 150 gold minimum, and pick up 50 to 100 gold (split among your team) for completing various tasks. It would have taken 7 games of typical play to reach that gold requirement, and the benefit really wasn't all that great. The designers have developed a system for long term play, working on the idea that a player could consistently show up and continue to actively pursue goals for a few years before they'd maxxed out their character. But the development process is slo-o-o-ow, I can see a lot of players leaving the game (and have already seen a few do so) because they aren't seeing any improvement or benefit for their attendance. Everyone is rouly equal, and those who've been there since the beginning are only slightly better off. It's a legitimate design technique, but the ramifications of such design need to be considered.
D&D 3.0/3.5 worked off the idea that 13 encounters would see a level of improvement in the characters. If a session consisted of 4-5 encounters, then every two or three games would see a level boost. When characters had the potential to gain 20 levels, that meant maybe 50-60 games in a character's career from green newbie to legendary hero. One level of increase in this type of game is fairly dramatic, as combat skills change, spells are gained, knowledge is acquired and other benefits added. So it's a pretty fast progression, it all depends on the types of stories you want to tell.
Point buy systems don't see general improvement across all categories, so I expect more chances for smaller increments of improvement. Instead of seeing six different areas get a +1 at the end of every third game, I'd expect a single area to get a +1 at least once or twice a game, or at least see the character change in response to the story being told (your response to the event has given you +1 here, but -1 there). I don't need character improvement, but do like to see character evolution and transformation. If a character isn't changing, what's the point of the story. Seeing a character transcend their starting level to become someing more powerful (something with stronger agency within the narrative) is satisfying, seeing a character make their mark on the wider community regardless of their power level even more so.
What am I basically trying to say in this post? It's been another meander through my current thoughts, and I like to see character development match the demographics of the setting. Improvement is good if there is scope within the setting for characters to move up in the power hierarchy, change is just as good if characters can affect the wider world in some way, or if their actions can be reflected in their self-transformation.
Just the things I've been thinking about lately.