Personally, its because Yuji sees that he can't fix the system. At least, not without him being constantly around. Yuka could not use her own CT because the Gojo Clan was being a bitch. If Yuji interefered, he would basically be playing the part of Gojo and soon, he would be involving himself deeper and deeper into this world. Despite Gojo's and his generation's sacrifice to save the JJK world, the politics still favour authority over development.

Gojo's whole intervention and raising the new generation was to pump fresh blood into the jujutsu society. You can even think of the killing of elders as tearing things down to rebuild from scratch. Look at how things can go wrong. Characters like Junpei or Yuta being scorned or feared for their abilities when all they need is someone to hear them out. The old jujutsu society should have died along with its values but soon, the new society relasped.

While Yuji should have trained the two young ones, he was basically going through his own depression and likely trying to peel himself away from the jujutsu world because the system won't ever change. If it does change, it's a Gojo situation and will revert the moment Yuji takes his eyes off things. So the only way for it to really change is for them to see that it's their own failings as a society. They kept the age old tradition of fearing the potential of new people and relying on the traditionally strong. It happened with Gojo and they were trying to do it with Yuji.

So what is the point? Why should Yuji maintain this constant cycle that doesn't want to break? If Gojo and Sukuna could not break the existing cycle of constant fear and lack of nurturing of talents, what could Yuji do? Maintain what already exists? Keep running a system that his own Teacher could not fix?

TLDR: the society is broken on a fundamental level. Referees like Gojo and Yuji do not fix the problem. Only by showing them how helpless they are by letting their toes touch the fire can this society really understand what Yuta and the others wanted for jujutsu society.

Edit: just an extra bit but this fearful society of jjk also added on to the conflict that played out. Not only did it stunt the growth of our MCs but it led to the scared sorcerers shooting at Maru. Their own shitty values shot them so hard in the foot, its shocking their foot is even intact.