In the original storyline, Renji Abarai had only realized this after being reminded by someone else. He finally learned the true name of his Zanpakuto's Bankai and, naturally, obtained the power of his Bankai.
Yinsen's sudden reminder to Renji Abarai was meant as a small experiment: would a Soul Reaper gain the corresponding power directly as long as the owner correctly called out the Zanpakuto's name? Or had Renji Abarai already met the requirements at that point, causing his Zanpakuto to unlock that portion of its power?
Through Renji Abarai, Yinsen learned that as long as Renji correctly called out his Zanpakuto's Bankai, he could obtain the true power of his Bankai—but he currently had no way to control that power properly. That seemed to prove there was a reason his Zanpakuto had not given him its true Bankai before.
Watching Renji Abarai release Twin Kings Snake Tail, spend only a short time barely gaining control over his Bankai, then impatiently rush off to get himself beaten up, Yinsen did not stop him.
There truly was not much time left. Ichigo Kurosaki was making one final effort, hoping to raise his power a little further.
But he awkwardly discovered that after releasing that Heavenly Chain Zangetsu state—which he did not even know counted as Bankai—his power had stopped increasing, as if he had reached a bottleneck.
Yinsen knew what was going on, but Ichigo Kurosaki had already made his choice. So Yinsen's advice was simple: "Don't even think about raising your power any further in the short term. Go do what you need to do!"
After several battles, Ichigo Kurosaki had a feeling that this would be the final battle in the Soul Society. Brimming with confidence, he finally arrived at the Sokyoku in time and blocked the fire phoenix