@Taynio-I guess that it is a difference in opinion then. Laws of the ninjutsu is more important than the need of Naruto having to keep his word. Laws of ninjutsu are created for the sake of not letting the characters in the series do whatever they want. If they do, it will be like this picture from fairy tail:
http://1-media-cdn.foolz.us/ffuuka/board/a/image/1362/78/1362788845277.png
by then if that happens it will be considered trolling.
I agree with you that Gai's death will make naruto fans sad. However, his death will capture the hearts and minds of naruto fans and also enable them to have a deeper impression of this series, which will in turn make this series a better success. People will also not drop this series that is about to end or just because of Gai died. Its just like a hero died protecting his comrades verses a hero saved from near death after protecting his comrades, which will leave the fans a better impression of the series after it ends? In naruto universe, Gai's death might trigger rock lee to futher awaken his potential and manage to open the seventh gate and become a good support to naruto and sasuke. Gai's death will let the shinobi know that even shinobi with no talents and with hardwork can also make a difference. Gai as a konoha citizen protecting the shinobi alliance together with his comrades from Uchiha Madara while losing his life in the progress and this shows the allied shinobi that regardless of their villages they belong to the same group known as shinobi. This will in turn have a huge impact on the allied shinobi forces and will better connect the hearts of the shinobi, making them more united as one regardless of their village. They will also learn ninshuu which in the end achieving the ideal peace of what the rikudou always wanted. Neji's sacrifice strengthen naruto's will to continue beliving his own ninja way and also the resolve of those within the Alliance to fight to keep the bonds they had, while Gai's sacifice unites them and also serves as a good reminder of not to fall victim to the curse of hatred.
As for Naruto breaking his promise, he had already broken that promise to bits when Neji died. However, kishi did came out with an excuse which is shinobi are the ones to endure and so on and so forth in chapter 616. The only thing Naruto can do right now is to not let his comrades efforts go to waste and save the bijuu by defeating madara and extract them out. By protecting and carrying on his comrades will, he is actually protecting them in a sense.