Brought to mind from the recent (-ish) 'Star Wars Adventures' comic "Destroyer Down", where the Interdictor we are familiar with is clearly identified as an "Interdictor-class Star Destroyer".
It's even named! The "Spectral".
What do we get re-classifying this as a "Star Destroyer"? Well, you can take the 7th Fleet Star Destroyer title, then. It helps make the support-mission Interdictors...a bit more support-y. Is that enough to matter? The Interdictor feels pretty far enough behind the curve I'm not sure that'd even help, really, but...I dunno.