Extremely big, yes.
I was too slow with my edit so I will repost here:
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Hypothetical Situation:
Coffee shop owner: "OK, that'll be .7865 DASH please. My address is Xkh65Rfk8...
Me: "OK, sent."
Coffee shop owner checks his wallet and .7865 DASH appear.
Is his response A) "Thank you, come again" or B) "Can you cryptographically proof you sent me the funds?"
That's fine when the business has large reputational constraints. Quite different when dealing with an actor who might be on the margins. Which would include most non brick and mortar businesses. That is to say if the reputational constraints are extremely dispraportionate than what you are discibing works fine. I.E. the difference in the value of starbucks reputation compared to the value of my reputation. However if the two parties are at all similar, than there exists a risk where if you accuse him of being dishonest, he can turn around and say no it was actually you who was dishonest, he is in a position to inflict equal damage to your reputation as you are to his. Cryptographic proof shows, atleast more clearly, who is in the right.
When NASA first started sending up astronauts, they quickly discovered that ballpoint pens would not work in zero gravity. To combat the problem, NASA scientists spent a decade and $12 billion to develop a pen that writes in zero gravity, upside down, underwater, on almost any surface, and at temperatures ranging from below freezing to 300 degrees Celsius.
The Russians used a pencil.