The aftermath was not quite what the participants in the drama had hoped.
There was never an official inquiry into the collision, probably because the Republic was carrying a treasure in gold bullion ~ knowledge of its loss might have precipitated a world financial crisis.
Furthermore, the outcome was positive, so people believed that all collisions of ships at sea would end so well.
Consequently the shipping world came to erroneous conclusions, and did not carry out the necessary reforms that might have prevented the disaster of the Titanic, or at least mitigated its effects.
First among these was the idea that in subsequent collisions there would be enough time to ferry the passengers to another ship, as had happened first with the Florida then with the Baltic. The conclusion drawn from this idea was that it was not necessary to carry enough lifeboats to accommodate all the passengers at once. This amounted to a considerable savings in equipment; furthermore, the appearance of the ship would be more pleasant, both from the decks of the ship and from shore, if there were fewer lifeboats blocking the view.
Together with the time question came the second conclusion, namely that the ships would sink slowly, if at all, so a redesign of the hull to become less vulnerable to side hits would not be necessary. Thus the Titanic was not equipped with a double hull above the water line.
Third, wireless would always be effective in calling other ships to the site of an accident, so no changes in the way wireless was handled would be necessary.
Specifically, if the Californian, which lay just to the North of the sinking Titanic, had had two people who could handle wireless communications, the one who was on duty would have heard the Titanic's distress call. Instead, Cyril Evans, the lone wireless operator on the Californian, had just gone to sleep when the distress call from the Titanic was sent out, so the Californian did not steam to the rescue until it was too late.
These are but a few of the misconceptions derived from the Republic-Florida collision that set up the next series of large passenger liners for disaster.