You do not have to pay for champions, you can unlock them for free using easily-obtainable Blue Essence. Paying to unlock champions is pay-to-progress, because it gets you caught up to everyone else faster, but doesn't give you a competitive advantage.
You say progress, but it’s kind of both an endless treadmill and you’re weaker usually by lack of options;
When I used to play LoL, like 5-7 years ago, I was playing a rate of like 3-4 hours daily, which barely scraped by the amount of essence needed to buy the next releases champion, let alone the runes system they had introduced at the time (don’t know if it’s still around) which had a fairly dramatic impact on the early game especially for specific characters.
That is, while technically the game could be played purely on free tier and eliminate any competitive advantage… it requires a lot of effort to keep up. Not nearly as bad things like FarmVille used to pull, but definitely enough to say that ponying up cash is eventually needed.
And having more options available to you (both characters and runesets or whatever they do now) is definitely an advantage, and a significant one at that
You don't need options. It's best to play around 3 champions for your main position, and 1 or 2 for the other 4 positions. That means you want around 11 champions in your pool. More than that is too difficult to improve with. Let's round that up to 16 champions and give a bit more flexibility and experimentation. This is all you really need, and you will get it very quickly. By the time the meta changes, or you've played it enough to consider changing direction, you'll have more champions unlocked.