The reason why Sanchez’s transfer hurt so much was because it was unexpected. Yet, somehow our fans assume that every top player not performing at his best at the moment will end up exactly like him.
Look at the most successful clubs of recent times. Juve took a gamble by signing old and underperforming Pirlo, who ended up being their best or, at least, the most important player of the decade. Liverpool signed flopped Coutinho that they later sold for a ridiculous amount etc.
Barca signing Davids, Fergie signing Larsson and even Cantona, that Leeds were get rid off... it often works, sometimes quite brilliantly. If we can sign him for free, we should go for it.