Jiraiya, Naruto, Hashirama and Kabuto were able to enter into Sage Mode. One who enters Sage Mode possesses more abilities than a normal ninja. Why did the Uchihas never try to learn Sage Mode? Is it because of the Sage of Six Paths dividing his power among his sons?
Sage Mode requires a large chakra pool. Most Uchihas can't learn it because of it.
According to Fukasaku, only those who already possess "extreme chakra levels" can utilise natural energy to invoke senjutsu.
The Uchiha never tried learning Sage Mode, because, they never wanted it in the first place.
Yeah, the Uchiha don't have a large chakra pool. But that couldn't be the only reason.
The first quality that comes into mind when taking the Uchiha clan for analysis, is pride.
The Uchiha's pride stems from their battle skills, dexterity, intelligence and most importantly, their prized Sharingan. The joy of the clan members when a Sharingan develops in someone, is boundless. They keep the Sharingan in very high regard and consider it as the ultimate weapon.
Due to the amount of consideration and importance the Uchiha gives to the Sharingan, it is highly likely that they felt there was no need for any external enhancement jutsu, such as Sage Mode.
Another (incomplete) reason could be the Sage of Six Paths. He was the only other person Indra Otsutsuki despised (other than Asura). And the Sage Mode being something that stemmed out from the Rikudo Sennin, that hatred indirectly and unknowingly influenced Indra's descendants.
Other than the good theories everybody else have already listed, my guess is: except Madara, Uchiha clan only focus on abilities and knowledge that came from their doujustu rather than look outside of their clan's specialties. This limit was something that made Madara, then later Obito, Itachi, and Sasuke stronger and different from their clan history later on.
Other than that, the whole length of Shippuden has been the creator wanking out powers for the Uchiha whole way 700 chapters through. Did he really need to give them another power they really don't need?
All of the people whom you mentioned (Naruto, Jiraiya, and Kabuto) were taught Senjutsu even though they were eager or not. Not sure about Hashirama because it was never mentioned in the anime or manga, but Orochimaru wanted to learn it and failed. You see, whether it is the giant snake, the great elder frog, or some guy from the Hidden Woods, where Hashirama must have learnt Senjutsu, should decide to teach you the Senjutsu. Some Uchihas would have tried and failed or gotten rejected.
Suppose Sage mode is about balancing out your inner chakra with natural chakra, doubling your body's total chakra. In that case, I think it logically stands to reason that Fukasaku meant that those with higher chakra reserves have less of a "sweet spot" when it comes to fine-tuning that balance. Ranking them with numbers let's say ninja like naruto and hashirama have a rank of 10 in terms of large amounts of chakra and ninja like Kakashi and Sasuke have chakra reserves in terms of 4 or 5. Naruto and Hashirama have more chakra to gain before turning into a toad giving them the ability to train more efficiently where as trying to gain the same amounts kakashi and Sasuke would end up toads. This means that rather than being completely useless at it it would take them more time to learn to sense the nature chakra because they would require far more breaks to protect themselves from toad petrification. I think it may be like others have said that rather it just wasn't on their radar.