The price does not play any role at all, it just so happens that Bitcoins are simply the most expensive and most likely there will never be a cryptocurrency with the same price as Bitcoin and plus the fact that you have Bitcoin simply because it is more reliable than other cryptocurrencies, that’s why they called it the topic is exactly that.
Bitcoin has an expensive price is not a coincidence, Bitcoin can have an expensive price because of the high demand and supply of Bitcoin also has an important influence on the price of bitcoin. Basically when something has limited supply and has a very high demand then it will make the price high, this is the exact reason why bitcoin has a high price.
You are right, bitcoin has limited supply and high demand, this is what makes the price of bitcoin very expensive. Especially after the bitcoin halving, the price of bitcoin should have risen high because miner rewards were cut in half, but why is the price of bitcoin currently struggling and experiencing frequent corrections? That's how unpredictable Bitcoin is