I don't think using bitcoin to pay rent or using it for any other business will help reduce world inflation. As long as fiat currencies remain the world's primary currency and primary yardstick, bitcoin will not be able to change inflation. It can be said that Bitcoin is a hedge against inflation, but it will be useful for bitcoin owners. Bitcoin cannot change the world's general inflation situation. Inflation is a huge problem and many factors are needed to control them, not just using bitcoin to easily solve inflation.
It is true, the means of you paying it doesn't really change, in a world where your rent is 200 dollars a month, you can pay that 200 dollars in dollar form, digitally send it, in gold, in stocks, in crypto, it doesn't matter because it's pegged to dollar that way. In a world where your rent is 0.005 bitcoin or something, and you keep paying that, then things are changing, but for now that can't happen because price of bitcoin changes all the time.
I think that should be the most important difference in the current situation. Inflation and using fiat will continue for a long long time, we just need to learn to use bitcoin as well as we hopefully could, that would give us the benefit and we will do a lot better with it without a doubt.