If one could simply "print more" Bitcoins, then it would quickly lose its value (this is the definition of inflation btw) because of increased supply. This is the main reason why, for instance, the USD has lost so much value in the last 50 years.
People invest in Bitcoin because they think it will increase in value, not because there is a limited supply. Lots of stuff is limited, but have no value.
Throughout history, inflationary currencies (ie currencies without a cap) have all lost their value and collapsed. This includes thousands of fiat currencies and will most likely include the ones we're using today.
You say that money must be inflationary for it to work?
Well, gold is not inflationary but has been used as currency for thousands and thousands of years. In fact, it was used as world currency up until 1971. Apparently gold worked, right?
Consider this... Two villages. One produce fish and the other coconuts. They buy from each other. They each have 10 Bitcoins each. Let's print more Bitcoins -- let's double the number of coins and give them out to each village! They still produce the same amount of fish and coconuts. What's going to happen now? Yes, the price of fish and coconuts will double! In effect, the value of each coin just got cut in half. That is the effect of (uniform) inflation. (*)
Or, simply put: If every person's bank account is doubled, then all prices will double as well. So changing the amount of currency uniformly like that is pointless. Nothing really happens.
But wouldn't a non-inflationary currency cause prices to drop (and, thus the currency value to raise)?
You're correct! But there are forces which work to counter that effect. Let's look at gold again:
On a fixed gold standard, prices would indeed fall slightly year by year. (By the way, this is fundamentally a good thing).
The reason prices fall is because the amount of goods increases due to increased productivity while the amount of gold stays the same. In other words, prices go down while the price of gold goes up. But (and this is important!) higher gold prices also gives gold miners strong incentives to mine more gold! So more gold is produced which enters the economy. More gold in circulation will eventually lower the gold price (and raise prices again) until miners don't earn enough and they stop mining. Which leads to higher gold prices (ie lower prices of goods) AND... the cycle repeats again.
And that is why prices on a "fixed" money base stays stable.
But what about Bitcoin?
The stuff you just read (above!) about applies to Bitcoin a well, but there is a huge problem:
The Bitcoin price is not even remotely predictable.
I agree that it wouldn't be wise to buy one pizza with Bitcoins today, when you can buy 10 pizzas tomorrow. You see, for us to call something money, it has to to be stable. Otherwise, it's impossible to make economic calculations. So until (if) Bitcoin becomes stable, no-one is going to use it as money for practical reasons.
So for the time being, you should consider Bitcoin an asset for investment, not money.
(*) This is extremely simplified, particularly as I ignore the harmful Cantillon effect. Inflation (money supply increase) in the real world, causes enormous amounts of problems, one of which is that it acts taxes the most unfortunate of us.