Interesting question! While we wait for answers, the following question may be of interest to you: The SS Californian was a little more than twenty kilometers away from the Titanic at the time of its sinking, why did the Californian not come to the rescue of the Titanic?, with an answer by /u/Second_Mate. It indicates that there was indeed a ship close by, and /u/WanderingSkunk basically remarks the same as you in a comment, that lifeboats would be used to go back and forth to a larger ship.

First of all, the fact that the Titanic took as long to sink as she did is a testament to both how expertly she was built and the unique shape/length of the damage she took. The iceberg cut a (comparatively) shallow 230ish foot long gash through it- like running a sharp knife's edge through wax. It gave the Atlantic access to 5 water tight compartments that bought them time until the water finally went over the water tight walls.

Compare that to the Lusitania and Britannic, both of which suffered at the hands of man made weapons (a torpedo and mine respectively) specifically designed to sink ships. There's still a lot we don't know about the Lusitania but there is the fabled "second explosion"- which no matter what caused it undoubtedly hastened it's descent. As a result of the explosion Britannic had one of it's watertight compartments damaged and had many of it's portholes open on it's lower decks which added new routes of entry. (Conversely it was very, very cold the night Titanic sank so most of her portholes were shut).

The Empress of Ireland had a few unique circumstances that caused it to sink irregularly fast. One being location of the collision and another being their failure to close the water tight doors.

Another thing you have to look at is how they sunk. Titanic is unique in that it sunk in calm water and completely (or almost completely) upright. Honestly think about every other sinking ship you've ever seen. They always capsize. Titanic didn't and as far as i'm aware that's the only time in history a ship that size has ever sunk that way.

You are also correct that the prevailing wisdom was that lifeboats would be used to ferry civilians. And though it's erroneously pointed to as one of the major reasons for loss of life, the fact is (and they knew this then), lifeboats don't equate to lives saved. I mean- just look to Titanic. As you've pointed out it took just under three hours to sink, in ideal conditions (calm sea and level) and it's last two lifeboats were still floated off deck. If Titanic had had more lifeboats. They wouldn't have had time to launch them all and most people believe more lifeboats would have actually gotten in the way and caused more lives to be lost (this is a different topic so i'll refrain from going into too much).

What led to this belief that ships would be ready and waiting for rescue when that was clearly not the case?

Multiple factors. One being the world wide adoption of wireless transmitters. Another was the fact that the trans-atlantic route Titanic was travelling on was incredibly well traveled. And you know what else?

It was the case. The Californian was only 15-20 miles away as the Titanic sunk. Close enough that Captain Smith ordered the lifeboats to row towards her lights, had distress rockets shot up to try and get her attention, and even attempted to use morse code lamps. Sadly, the Californian's radio operator had gone to bed a mere 25 minutes before Titanic sent out her first distress signal.

So there you have it. Lifeboats don't guarantee live's will be saved. And if your ship is sinking slow enough to launch all the boats, there was almost definitely enough time for another ship to pick them up.

Hope that answers your question. I run /r/rms_titanic. Please join us!