The reason infinity $100 bills is more valuable than infinity $1 bills: it takes less effort to utilize the money.
Let's say you want to buy a $275,000 Lamborghini. With $1 bills, you have to transport 275,000 notes to pay for it. That will take time and energy. With $100 bills, you have to transport 2750 notes. That's 100x fewer, resulting in a more valuable use of time and energy.
Even if you had a magical wallet that weighed the same as a standard wallet and always a had bills of that type available to pull out when you reach in. It's less energy to reach in a fewer number of times.
Let's toss in the perspective of the person receiving the money, too. Wouldn't you rather deal with 2750 notes over 275,000, if it meant the same monetary value? If you keep paying in ones, people will get annoyed. Being seen favorably has value.
You couldn't buy that car with either denomination since money would have zero value now... and also the universe would collapse in on itself... but mainly the zero value thing.
Fair, but there's also a lot of businesses that don't accept $100 bills which would make paying for smaller everyday things annoying, and realistically I don't think any car dealership would want to deal with 2,750 $100 bills either. Besides, with infinite money you could hire people to count and move the money for you, if it's $1 bills instead of $100 bills you simply hire 100 times as many people!
I think it would be easier to go to thebank now and then to exchange some of your $100 for lower value bills than to do the opposite.
Besides, if there are places that don't take bills less than $20, there are a lot of places that aren't going to let you pay with only $1 bills. I can't imagine a car dealership letting you do that. Or if you want to buy a home, etc.