Client's attention - is one thing on which you can't compromise.
Public places have limited space and noisy surroundings. Imagine the extra effort your client might be putting in to stay focused.
Could you afford to compromise your client's attention?
You definitely don't want to test your clients' patience over the slow internet in public places.
Do you really want to count on wi-fi stations of public cafes or your mobile data on your first meet?
One way is to show static slides and images to clients. Another way is to tell your story step by step alongside helping them to visualise your value over a whiteboard.
What do you think is going to leave clients with better impression?
This is the bottom line.
Coming across as a serious and professional person leads to having them trust you. Unfortunately, if they felt you are not the professional they can count on, well then start hunting for another fish :)