Conte was actually being backed though. The club went after Sandro and Koulibaly in the first season, but both clubs refused to sell those players so we got the second choice (Conte's second choice) in Alonso and also Luiz, as well as Rudiger. Conte also got Kante (the league winner the season before and arguably Leicester's best player behind Vardy) and Conte also had the fortune of a 20 goal a season striker in Costa too, who he managed to have a spat with and ruin the relationship with so much that Costa wouldn't return. I can understand the club's stance form that point and it wasn't positive. Conte had it pretty well in that first season if you ask me.
So Conte wanted Sandro and Koulibaly but didn't get them? Whereas Sarri gets Jorginho, Kepa, Higuain, Kovacic... All his picks to play his system.
I've made the point elsewhere, Kante was a big coup but after his season with Leicester he was still a somewhat unknown quantity. At that point in time he was a one-season wonder and we paid a relatively modest sum for him making a somewhat low risk gamble and fortunately he was able to replicate his form and became the start he is today.
Conte didn't have a good squad for his first season, Ivanovic and Terry's legs had gone but they were viewed as first choice going into the season. If you ask me he turned water into wine by converting Moses, a rather underwhelming winger, into a productive fullback... None of use saw that one coming. Throw on top Alonso, the former Bolton and Sunderland leftback who'd be plying his trade at a mid table Fiorentina turning into the best left sided defender in the league. If he'd have got his first choice in Sandro and we got those performances you'd have been happy... but from Marcos Alonso? That was good coaching.
He also got David Luiz playing some of the best football of his career by putting him the centre of a back three, maximizing his strengths but protecting his weaknesses.... Not forgetting he achieved this off the back of a very short pre-season having changed formation and tactics after the season had already begun. Completely disagree that Conte had it good transfer wise during either of his seasons personally.
As for Costa, he had been angling to leave us from the first season he joined Chelsea. That he stayed for three seasons was surprising. He had his head turned by a big money offer from China and it was all downhill from there. Yes Conte didn't cover himself in glory with how he handled but I don't think he or anyone else was going to convince him to stay for a forth season.