Why do government inflate the value of currency by printing more if printing more does nothing to increase the buying power that government has?
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The goal of the government (the central bank) is generally to keep the value of money slightly decrease over time, and one way of doing that (although not always that effective) is to print more money.
Why do they want the value of money to decrease slowly? Because it encourages people to make use of it. Money is useless in a mattress, but very useful if you invest it or put it to the bank.
Why is it not always effective? Because contrary to popular belief, the government is not the only one to “print” money (it is the only one to print cash, but not other kinds of money). When you go to borrow money to a bank, they don’t take it from somewhere else and give it to you, they literally open a new account with money magickly on it out of nowhere. It’s different from the government printing money, since there are rule on how much they’re authorized to create, and the newly made “fake” money (scriptural money in economic terms) with disappear just as magickly as it appeared when you pay back your loan. Because of that, the government only has limited control over how much money is out there, and therefore how much money is worth.
Also, money supply is only one of the things that influenced inflation. Supply and demand of goods also influence inflation. After all, inflation is just the price of a given basket of goods, and those goods can change prices for many other reasons (like a pandemic, a war, other economic issues, etc).
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