Whether we say "at this level" or something different like "in the PL environment", the question will always be there until he does well in the PL. That might be with or without us.
I actually don't think Conte was cut out for the PL. As a player, manager and international manager he had spent all but the 2 Chelsea seasons away from Italy when he joined Spurs. In his first season, he picked up Jose's amazing squad after the club doctor fiaso, and he disrupted the PL by playing 3 at the back and wing-backs. By the second half of the season Poch just matched him up and Dele did the rest. By Conte's second season he totally crashed and burned and didn't even make top 4. When you think about it, he did a mini version of that with us. He got us top 4 and then totally crashed and burned second season. He tried to implement his Serie A winning system in the PL. It failed badly eventually.
The thing is nobody said "at this level" about Conte but it was sort of true. The PL is much stronger than Serie A. As for Ange, he has never operated at this level including his domestic and international experience. The question is a totally fair one whether he can operate at the PL level as it also would be if he took over at somewhere like Athletico Madrid. La Liga is also a very impressive league.
What I think we've seen is a very good tactical system that needed adapting to the new environment and especially around the current players at his disposal. It didn't need major surgery, just some refinements. Ange would never experienced such effective counter play every week from the leagues he's operated in. The quality of football technicians is at a different level. It was totally there for him to reinvent the next generation of his football philosophy. Pep did in his second season. He studied what was happening and refined it. He has never stopped refining it to keep things fresh.
Ultimately, Ange has appeared to have chosen not to and just stuck with his prior methods. So did Conte. There will be no surprise in his exit from the club.