Why don't you get an invoice for eating in Japan
Because diners don't need invoices. Invoices can be issued. But it may not be of any use to you. Tax refunds are definitely not available. Simply put, all purchases you make in Japan can only be refunded if they meet one general principle: items that reach a certain amount of money and are not used or consumed until they are taken outside of Japan. This means that you can't get a refund if you eat at a restaurant, buy a lunchbox at a convenience store, buy a drink at a vending machine, go to a movie, stay at a hotel, etc. In fact, you can't get a refund if you buy a drink at a vending machine.