I don't think it's a knee jerk reaction, Gasperini doesn't really get the credit he deserves outside of Italy, three 3rd place finishes in a row, two times runner up in the Coppa Italia. Doesn't really have the budget to compete with the likes of Juve, Inter, Roma, Milan etc but he still manages to in terms of top 4.
Initially when I made my post about potential replacements I did think about putting him in, but the list of maybe's generally included people who had won something. It would be a left field appointment but not necessarily a bad one.
Only thing I would say and this is why I didn't suggest him is previously Klopp was a very obvious appointment. It didn't take a lot of looking at underlying statistics to realise that appointing the man who broke Bayern's dominance with a low budget and great attacking football was going to be the best decision for Liverpool. I think the club will look for something or someone similar and Gasperini probably won't make it that far. But it wouldn't surprise me if they'd already had a good look at him