No. It does take away the need for trust in a very limited sense, in that I don’t need to trust you to know that you have paid me. One other possibility is you could fake a note, and I would have to trust you have not given me a fake note - and I don’t have to have that trust with blockchain anymore.
But trust is still required in society. If I am paying you for my pizza, I have to trust you to make that pizza with the right ingredients, and there is no way that blockchain is going to help me there. I still have to trust you to not spit in my food.
But in the very narrow sense of transactions, we could get rid of the need for trust with blockchains.