D1.1 shows ER80S wire as being prequalified for Group III base metals. A572 grades 60 & 65 are listed in that group but A588 is not.
So if all your welding is on Group III steels then you could have the ER80S as a standard shop wire. If you weld on Group I or II steels, then it would be overmatching the filler metal.
But if you have qualified the combination, and your customer has approved it, you could use the ER80S. Just realize that you could not represent your welding as pre-qualified per D1.1 and that each customer would probably require you to submit PQRs.
From a practical side of things, I would think you might experience more problems, such as cracking if you use the wire on Group I & II. It might not be worth the trouble due to qualifications and weld repairs.
Chet Guilford