It is really easy to create and send an invoice. You can store addresses for future use, add notes, etc. The invoice itself is clean, easy to read, and easy for the customer to pay. You receive an email when the invoice is sent, and another when the invoice has been paid. Money from your square account can be deposited into a bank account (automatically) the next-day for free. (Instant deposits are available for 1% of deposited amount.)
Processing fees - but they are unavoidable. For invoices the fee is 2.9% + $0.30 compared to keyed-in cards which is 3.5% + $0.15.
Square Invoices is very easy to use, and has an updated, clean look. While we haven't needed much support, when we have had questions they have been very prompt and helpful! Also, being a consistent customer has it perks - they often involve you in promotions (like free processing for $1000 in sales) or free chip-readers.
Rather than keeping cards on file (which we would charge through the square app anyway) you can have the customer pay at their leisure. With so much credit card fraud and the subsequent changing of card numbers, it is hard to keep active cards on file. Rather than trying to track down the customer for an updated card number, it is easier to just send them an invoice so they can pay when they have a chance. Less work for both parties.