So if you flew into, say, Milan Malpensa onto 35R as a visual approach would you do the G/A for ILS Y or ILS Z......they are different!
Having never flown in Milan, I can only assume that the ILS X & Y have different minima (as would be the case here in the US). Also assuming that the ATIS would specify X or Y, that's what I'd load in the FMC and what I'd be flying.
I look at it from an ATC perspective. Let's assume worst case scenario, and we lose coms on the GA. If i fly the published missed, at least ATC knows where I'm going, and where to protect airspace. If I decide to do a pattern, there are way more variables. How wide will it be? How long will the final be? What if there are clouds at pattern altitude?