It's Batman. He also didn't carry the nuke out of Gotham on his back, he used his Batplane. Beating a villain with gadgets is Batman. Having the humility to recognize that he can't physically beat that guy and has to rely on technology instead wouldn't have turned it into a different film.
Yes, it would have, since Batman's whole arc in this movie is that he has to let go of his death wish in order to defeat Bane. Before that happens, he's brutally defeated, and after that, he wins the day, saves everyone and finally moves on with his life. That's what the movie's about.
"Batman defeats Bane using gadgets" is a different movie, one that I personally feel is considerably less interesting. You may have a different opinion about that, but when all is said and done it's still a different movie.