I see Franky's unmodified back as an extension of his personality and character. In the past, he didn't modify his back because it was difficult to do work on his own back. Now that he probably has the ability to do work on his back (I don't see how couldn't have this ability, what with Vegapunk's old lab accessible to him and all the modifications he has now made on himself), I like to think that he just didn't think to do so - he isn't used to working on his back, and so neglected doing so.
Kind of like most weight lifters - all chest, shoulders, and arms, no legs or back. I mean just look at Franky's legs. Just look at them. He looks like every idiot at the gym who I, nonetheless, desperately hope never wants to punch me.