This is basically modern AAA gaming in a nutshell, not just TR. Uncharted, Last of Us, Halo 4, GTA, The Order, etc, they all want to be blockbuster movies. There are exceptions, like Sunset Overdrive and the Ratchet games, where they don't take themselves too seriously and try to add some humour instead while still having very solid gameplay, but honestly, for the most part if your focus is gameplay and the serious stories annoys you then you really shouldn't bother with the AAA games anymore, go for indies or retro games instead, or maybe Nintendo games.
Me, I kind of like this game style, I loved The Order 1886, Beyond Two Souls, Last of Us, Tomb Raider, Halo 4, etc in many ways _because_ they had so much focus on the movie scenes, stripping away all that and they would all be kind of bad. TR, Uncharted, Last of Us, The Order would all just be Gears of War cover-based shooting with some Prince of Persia climbing and jumping in between. Nothing wrong with that, but... Been there, done that. :/ Add a story, some nice characters, a story twist, a nice finale, and they suddenly start to feel fresh again.
The stories and the acting is usually bad compared to real movies though, and I agree that it gets worse when they're trying to be really serious, but I'm a huge movie nut too and I'm not only watching the imdb 8.0+/10 movies so playing these type of games on a projector screen is actually nice and not too far off from watching a regular 5/10 action flick, which usually have the same problems in serious scenes. I still like retro games more when it comes to gameplay and definitely play more retro games than modern games these days, but modern AAA games still manage to get me entertained too, just not for the same reason. Nothing wrong with that, in the end it's just entertainment.