As for BNB and Cardano, you are right that it is not about the amount of coins the project has created. However, you are wrong, because it is not about "trading volume" but about the market cap, i.e. the value of the entire project = the value of all coins, not the amount of all coins.
And you are right, because as individuals we can't do much. It will be whales who will determine who will be in 3rd position.
I feel like the hype around BSC is not really as high as it used to be few months ago, BNB is still wanted and used everywhere but it requires some amount of being used, whereas Cardano is a coin that is all by itself standing there, not like BNB where it requires other projects under its belt to succeed as well. Basically what pancakeswap did (and all the rush towards to other ones after that) caused BNB to end up being this high, and that is not something cardano has.
This means that it is both good and bad for cardano, where cardano could stand all its own that is great but bnb could increase with the help of so many that is great for them. Which is why I think there is a good amount of rivalry and both sides are actually quite deserving to be there. I believe BNB deserves a bit more, because it is so much bigger outside of being a coin as well, but I would understand ADA as well.