I actually think they'll get in. Probably not this year, but eventually.

I recently watched a podcast with Chris Jericho where he had Eddie Trunk as a guest. And Eddie said something I hadn't known before - once an artist gets inducted in the HOF, he/she also gets a vote. As a result, the snobs that created HOF and try their hardest to prevent the bands they don't take seriously from getting in (e.g. Bon Jovi, Iron Maiden, Def Leppard, Deep Purple, Kiss, Hall & Oates, etc.) are gradually losing their influence as the total number of voters increases. I think it's a big reason why we have seen inductees that we didn't previously expect (Kiss, Hall & Oates). Thus the more poppier bands get in, the more likely it gets that Bon Jovi does too.

"When?" is the question I don't particularly care about, because they (Jon) are already past the point of sounding decent in the induction performance (the ship sailed in 2013), so the only value will be the nostalgia from seeing them playing with Richie (and maybe Alec) together, which will still be relevant.