We are currently taking payments onto sales orders via the prepayment feature. Then when we invoice the sales order the prepayment we took on the sales order automatically attaches to the invoice created off of the sales order. 

So why can the payment link payments not be recorded in the same manor as the keyed payments processed as prepayments off of a sales order?

These are indicial process. The only difference is payment link payment is the customer is entering their payment information and the prepayment off of a sales order is being entered by a employee.