My opinion is that it seems to be the case.
Before she died, Kushina proposed that she should pull Kyuubi into her body and die together with Kyuubi. Mainly based on two principles, 1. If the tailed beast is extracted, the jinchuriki will die, so Kushina thinks that she is about to die. 2. When the jinchuriki dies, the tailed beast in the body will also die. Kushina wants to kill the nine tails based on this principle. However, a new principle was added in the later period. Once the tailed beast is extracted, the jinchuriki will not die if he seals the tailed beast back before he dies. Therefore, if the Yondaime listened to Kushina, neither of them would have to die.
The main reason is that the fourth generation was too brave to sacrifice and even irresponsible. He already knew that there was a man behind the scenes who coveted the Kyuubi, and dared to seal the Kyuubi into the defenseless Naruto. It was simply asking Naruto to die. Fortunately, Obito had been idle for 13 years, otherwise the Fourth Generation wanted to let Naruto control the power of the Nine Tails, and it would have been impossible to defeat the mastermind behind the scenes.
He also said that the balance of the power of the tailed beasts should be preserved. That can't be sealed into Naruto, then he won't be able to exert his fighting power for more than ten years. It's better to just let Kushina and Kyuubi die together, and then catch Kushina after Kyuubi is resurrected. Or at least seal it into a young man to ensure that he can exert his combat effectiveness.
As for the fourth generation, they used a barrier to shut out the third generation and prevent others from interfering. He secretly gave Kyuubi to his son. Kyuubi is public property.
But if the fourth generation had not died, there would have been another outcome. The Fourth Hokage was good at developing ninjutsu, and the Rasengan was the ninjutsu developed by the fourth generation. However, due to his untimely death, this jutsu was not developed. Later, with the efforts of Naruto, the jutsu was developed on the basis of this jutsu. The property changes were added and upgraded to the Rasengan Shuriken. Later, the Rasengan Shuriken, the Tailed Beast Rasengan Shuriken, etc. were developed. However, these were all developed by Naruto who was not good at developing and improving ninjutsu. If Minato Namikaze was good at developing and improving ninjutsu, he might have improved the Rasengan into other more powerful moves.