I'm not sure if there is such a specific fanfiction. Fanfiction can cover a wide range of very creative and sometimes out - of - the - ordinary ideas, but this one seems rather unusual. You might try searching on some large fanfiction websites to see if it exists.
The chances are probably quite low. This is a very specific and rather unorthodox concept that might not be very popular among fanfiction writers. Most fanfictions tend to focus on more common themes like character development, new adventures, or different relationships within the bounds of the original story's feel.
One consequence is a change in his physical strength. Kurama provided Naruto with a huge boost in power, so without it, he might not be as strong in terms of brute force. However, this could also force him to become more strategic in combat.
Well, Naruto might gain new and powerful jutsu. Kurama could teach him some unique chakra control techniques that no one else in the village knows. This would make Naruto even more formidable in battle.
Kurama might develop from being a more aloof and powerful entity to one that has a newfound sense of connection and responsibility. He would have to care about the well - being of Kushina and the unborn child. Kushina, on the other hand, would have to deal with the physical and emotional changes of pregnancy while also coming to terms with the fact that it was Kurama who was involved.
Naruto would likely become more powerful. With the Yin Kurama, his combat abilities could increase significantly. He might also become more mature as he has to deal with the added responsibility of this new power. For example, he would need to be more cautious in using it so as not to harm others accidentally.
If Naruto gets rid of Kurama in fanfiction, one way it could change the story is that Naruto would lose a major source of his power. He'd have to rely more on his own natural skills and training. This might make him seem more vulnerable at first, but it could also lead to him developing new and unique abilities. For example, he could focus more on his Sage Mode training and become even more proficient in it without Kurama's chakra interfering or overshadowing his progress.
It could also transform his ability to interact with the tailed beasts. Naruto would have a deeper understanding of the nature of tailed beasts and their powers. This might lead to him being able to communicate more effectively with other tailed beasts, or even borrow their powers in a more efficient way. He could potentially use this knowledge to find new ways to calm down enraged tailed beasts and prevent them from causing destruction.
For Naruto, it would be a whole new experience. He'd be constantly trying to communicate with the mecha Kurama, learning its quirks. Shikamaru might be the one thinking about the strategic uses of mecha Kurama in battle. He'd be coming up with plans on how to best utilize it. As for Kurama, he could be in an internal struggle. Part of him would want to stay relevant in Naruto's battles, while another part would be curious about this new mechanical version of himself and how it could help Naruto in the long run.