I don't think he had favourable conditions at all, especially when we get specific. The 14/15 team was built in Ivanovic in his prime, a duo of Terry and Cahill playing close and deep with Azpilicueta staying close to Terry to offer mlre protection against lack of pace. Matic was still in the best form since we bought him the January before and Hazard was pfa quality as was Costa. However, as most chelsea fans know, by the turn of the year, we were spanked 5-2 by spurs and the rug unravelled. Matic form took a dip and never recovered. Fabregas' defensive frailties were more and more apparent. Costa's goals dried up and Oscar (like always) became a toothless number 10 by December. Mourinho halted the slide by playing incredibly defensive football and relying on Hazard for the second half of the season.
The next season wasn't an abrupt dip. It was a continuation of the form we had been seeing since January. Matic seemed to be in permanently bad form, Oscar was still toothless, Fabregas was still someone you could walk past with the ball except now Ivanovic decided to be one of those players who get to a certain age and then collapse. Terry's decline wasn't much slower. Cahill was seen to be quite a liability when he isn't camped in his own box with the play in front of him and was dripped for Zouma. So then we didn't even have a solid defence to rely on when things went to shit like the title winning season.
This should all be apparent in Conte's first few games. Ivanovic was still almost laughable defensively (it pains me to say, he will always be a legend) Terry was still lost at sea a few moments a game and Cahill was still a liability. Fabregas was still a ghost defensively and so wasn't even in the team. Oscar was obviously considered a poor number 10, given more defensive duties to at least compensate. But being a yappy dog pressing defenders doesn't translate to being solid in CM.
Conte didn't inherit the defence that won the title. He inherited the drastically declining version. He didn't inherit the midfield that pulled all the strings either, but a poor imitation. There's a reason Luiz, Alonso and Kante were bought.
One thing I sill say is that Conte got the title winning Costa. It was only because of him that we won the first 3 games.
This is why Chelsea fans already think he is the real deal. He won the league with Victor Moses, [Irrelevant point] and David Luiz for crying out loud. Cahill is still a liability, just check the firsr few games of the season. But the formation hides his many flaws and puts him in a position to do well. As it does for Dave, Luiz, Moses, Alonso, Kante, Hazard, Pedro and Willian.