Even though it doesn't contain all of my favourite songs and it's not my favourite tour, 7800 Fahrenheit is the Bon Jovi album that I can listen to every day of the week, therefor every time I'm asked what is my favourite Bon Jovi album I always go for Fahrenheit. I really, really love that album, but I'd be lying to myself if I said I don't think it's dated, or that the production is on point. I'm not sure how much objectivity matters in a discussion as subjective as music preferences, but from the former perspective, it's really just not great.

'I genuinely think it's the only album where you can say "Here, this is Bon Jovi the band as a musical unit that does its own thing".'

I can't say I fully agree with this, but I do see where you're coming from. The first album was mostly Jon Bon Jovi getting a band together to play his songs; even though the rest of the band were involved in the majority of the production, it's very Jon-esque and you can have a person who doesn't know the Power Station Years listen to those tracks and they'd most likely say they are outtakes from the first album (well, in some sense, they are), so from that perspective 7800 is definitely more Bon Jovi than the debut. And while you're right that the later albums were more constructed, I don't see why that would make them any less "BJ doing their own thing", and I'd like to explain that with my actual counterargument: 7800 Fahrenheit was rushed.
Jon always made it seem almost like an overnight task and while I'm not sure how much of that is true and how much is him overselling it a bit, simply doing the maths does conclude that it was at least rushed enough for one to lose all reason to consider it 'BJ core', even if we narrow it down to the 1980s. They didn't have time to do their own thing.

'The album that should have melted the face of Rock but, for whatever reason didn't.'

I expect a lot of people to jump at me for this, but realistically SWW (maybe NJ too, but to a lesser extent) is the only one that did that, ever. It has 2-3 absolute rock anthems that took the world by storm and will never leave relevance, what does 7800 have in that regard? In And Out Of Love? Only Lonely? Yeah, they're great songs, but for the general audience, it's just fun songs to hear on the radio during the short time they're 'popular' and maybe turn up the volume to, but nothing more than that.