If you want to see these as Sales, you use Sales Receipts. You only use Invoice, because you want to see it as sales and to reflect they owe you and that you are anticipating the payment arriving later.
If you simply want to "do banking" as income, you don't have Sales data.
If you charge customers sales taxes, and don't use sales transactions and simply use the Banking tools to track this as income, you would be reporting Tax collected as your income, which means your own taxable income is higher for funds that were not your income. That is always a problematic situation. No one likes to pay income taxes on funds that are not your income.