Inflation does not take money out of your account: it takes away purchasing power. If prices rise 3% a year, the $100 you hold today buys the equivalent of $97 next year, even though the balance still reads 100.
This is why holding cash is not neutral but a slow loss. An account paying nothing, against 3% inflation, loses roughly a quarter of its purchasing power over ten years.
Hence the practical distinction between saving and investing: cash protects short-term liquidity, and assets protect long-term purchasing power. Both are necessary; confusing the two is what gets expensive.