"Why do we need blockchain?"
Because blockchain (or DAG, the modern, scalable alternative to blockchain) does not support or allow:
1) One actor printing money for themselves out of thin air, stealing everyone elses' purchasing power in the process. Most people do not recognise this as theft, or even recognise that it's happening to them, but it's a serious problem. Most fiat currencies have collapsed in value since the 1970s.
2) Debt-based currency, which by definition and the cold, hard rules of mathematics, can never, ever be fully repaid. Only the principal is ever created (and borrowed) - the interest due does not exist, so this demands never-ending growth, simply to satisfy an ever-growing debt mountain. Interest is also exponential by its very nature, and anyone who truly understands how the exponential function works with currency supply will know that the ending of the story isn't pretty.
3) Frozen accounts, money grabs, sanctions, abusive politically-influenced blocks on payment processing (Wikileaks), or any of that nonsense. The amount of criminal activity condicted in USD dwarfs the entire cryptocurrency market, but if politicians ever took that as seriously as they purport to take crime committed with (or using) cryptocurrencies, they'd ban the USD overnight.
4) Payment reversal, clawbacks, et cetera. You know when you're paid, that's it: No ifs, buts or maybes.
5) Socialism. When governments are not allowed to simply borrow money printed out of thin air (and are forced, like in the old days, to balance their books), you will see massive cutbacks on unnecessary, inefficient and harmful schemes that only serve to discourage meaningful employment.
6) Cronyism. When those that can print money out of nothing are no longer allowed to do so, they may no longer abuse that power to buy governmental influence (lobbying is just a nicer word for corruption), putting them on equal footing with the rest of us. That's healthier for all of us in the long term.