Pedro not delivering in big games is weird accusation mainly because the reason he got his break/quite bit of attention with Barca last seasons is because he has scored in most finals/big games he has played in almost (except the WC final), late min goal in european super cup, world cup for clubs, CL games (against Inter), el classico and so on (became first player to score in 6 competitions in one seasons). He has scored several clutch goals for Barca.
He is certainly not one of their better players, but certainly not someone who rides on the talents of others, blends in well to their team and has good qualities and shows it. Carries his weight by being quiet role player who scores/assists now and then. For an attacking midfielder, has pretty decent goal turnout/productivity for them. 23 goals last season, 20 goals so far this season (also as impressive, 10 assists this season so far). Undeniably a good player.
He is weird hate object because he is fairly quiet and unassuming on the pitch, performs well enough in general, he isnt an annoying hack like Valdes, and IMO your description fits way better for that little twerp Busquets then Pedro. Who is EXACTLY like their version of Marchisio, he doesnt do much, perform that well, but just does the necessary, like Marchisio. But unlike Marchisio, he plays with almost entire lineup of world class players.