I think it depends on the movie, Guardians of the Galaxy felt pretty sincere to me, as did a lot of Captain America's outings, it seems to me like most of the solo movies are more meaningful than the team up event movies. I mean look at Black Panther, you had a radical Wakandan who was exiled for something his father did, and was in so much pain he wanted to cause revenge on Wakandans and the world outside of theirs, and there was a touching scene where he got to see his father again though a flashback and his father realizing how much pain his son was in.

Then there's also Guardians of the Galaxy where Peter got to remember his late mother, got close with Gammora, even Groot and Rocket's friendship was shown to be meaningful, and ultimately it was their bond as a team that saved the day.

This article as a whole just seems to basically boil down to "Marvel movies aren't sincere, Spiderman and Wonder Women did it better." and they give one poor example. I say MCU can do emotional and sincere moments, it just depends largely on the movie, I still remember the sincere tension in Civil War when Tony finds out what Bucky did to his parents.