Bitcoin and other cryptos do not work like traditional money, and it isn't just because they are appreciating in value.
Investing in a crypto is really investing in its underlying network. In order to use the network, one requires that network's respective currency. Consequently, the more valuable the network becomes, the more demand there is for its native currency.
Likewise, the more valuable bitcoin becomes, the more secure the network becomes and the more demand there is to use the network for crypto-economy projects. We haven't yet seen this demand fully express itself because the scaling war slowed Bitcoin innovation and prevented it from fully opening its doors to realize the demand, but once it does I expect a massive flood into bitcoin. We know the demand is there, look at Ethereum, and once bitcoin makes itself available to that demand it will be a sight to see.
So investment into Bitcoin is essential for its growth, and its growth is essential to the use of its currency.
The stronger Bitcoin's network becomes, the more projects and economic infrastructure depends upon it, the more the value of bitcoin becomes entrenched. Once it is understood that the only way for the value of the currency to be destroyed would be for its respective network to be destroyed, and when that network grows to the point of becoming indispensable to society in a way similar to how the internet is today, the reliability of bitcoin's value will seem as secure as the value of the US dollar. At that point one will actually be able to say that bitcoin has something akin to "intrinsic value" -- i.e., the concept that a money has value even if it ceases to be used as money.
So it is essential to Bitcoin, and all cryptocurrencies, that its underlying currency be deflationary, at least during the growth phase.
It is also important to point out that the crypto-economy involves many competing currencies, so we are dealing with a fundamentally different beast than national economies that rely on a single currency. Because anyone is free to print their own money in the crypto-economy, it is vital that the base currencies be deflationary.
In fiat systems, you want a small amount of inflation to encourage lending and discourage loan defaults. When banks lend money, they do so by "printing" new money into existence. What prevents the system from spiraling into hyper-inflation is that money is destroyed when people repay their debts. Because there is always more debt in existence than money (since debt = money + interest) there has to be a constant rate of inflation to allow there to always be enough money to repay the debts.
In the crypto-economy, by contrast, new money is printed into existence without usually having a way of being destroyed. This problem is obviated by the fact that new money usually comes in the form of new types of currencies, it isn't a printing of existing currencies. If someone wishes to print new money, for instance, they must create a new token, give it a new name, and sell it (e.g., through an ICO). The money supply of existing currencies isn't being affected by the expansion of the money supply in the crypto-economy.
What this means is that the crypto-economy itself must discourage over-exuberance since there is no risk involved in creating one's own currency. That discouragement comes from the fact that established currencies are deflationary, and therefore new projects must be able to prove that they can outperform existing platforms. Because the crypto-economy is a competitive free-market, competition between currencies makes it so that monetary policy from a single institution aimed at artificially recreating the conditions of a free market is not required.