Games should strive to tell their story through the gameplay first and only resort to other options when that's not possible (and even then, consider a story better suited to the medium).
I agree as well, but there are setpieces and interactions that are simply impossible to convey through gameplay. Even the likes of Half-Life originally had a few cutscenes, one including a female scientist that was supposed to betray you to the marines, but those had to be scrapped due to time constraints. Did it's removal have any impact on Half-Life's barebones plot?, no, but it shows that even Valve felt some cutscenes were necessary to add flavor to the game. Even that one scene where you are dumped in the trash compactor was a cutscene, not gameplay. I can think of many moments in games that simply wouldn't click as well if it were told while I was shooting at monsters, or walking along a corridor. I also do not think walls of text are an appropriate way to tell a video game story either, far too static and dull for an interactive medium.
I will say the last time I enjoyed ANY story in a video game was Left 4 Dead 2. That game does exactly what you are saying, as the entire game's plot is told through humurous character dialogue and the environment. But it works because it doesn't take itself seriously, it's not trying to be another "Walking Dead" or "Dawn of the Dead" style rant against mankind. The exact opposite to Left 4 Dead 2, is The Last of Us. Which was written by a jew and tries to take itself TOO seriously, and as a result is loaded with cutscenes and subversive themes. Cutscenes are the game, in essence.
So to me it's a balancing act. Remove as much unnecessary chaff and bloat from the game as possible, but where necessary add a few short cutscenes to add a bit of "punch" to the game.