The idea of bitcoin being finite is not the real reason why we care about the price of it. The real reason why we think it worths something is the fact that nobody controls it. USD or Euro or anything else could become less valuable due to inflation all because there are people at the top who make it so. But, bitcoin is not touched by anyone or controlled by anyone and that is why we care about it so much.
I would rather lose all my money in bitcoin, then keep it in dollar and have it slowly become less valuable. Any investment made in fiat would be racing towards inflation and hoped that it wouldn't be this low, and that's why there is crypto, it's the main reason why it was created.
This is what the people are counting on. There is no inflation with it, and yes there is a "little" inflation in guise of mining rewards but that is nothing compared to how much money we are talking about. And that means we are going to be pretty upset when we find out that fiat doesn't have that at all, billions do not still realize that.
You could literally print money to make dollar worth 1 cent euro, but they won't, yet they "can" and that is the scary part. If we are going with the fiat route then we are going to regret that forever because if you go back 10 years, 20-30-40-50 and you will realize that things only get more expensive and crypto is a way to protect that.