At the time, the Titanic was the largest and most luxurious ship ever built. It was clearly more expensive than any previous civilian ship and had the latest technology and civilized conveniences. So how were lower class passengers able to afford tickets? If you look at today's ships, many low income households can not afford even the lowest level of accommodations on a cruise. Yet, there were over 700 third class passengers aboard the Titanic, more than first (319) and second (272) combined. This would seem to be wasted space for a ship that costs so much to operate and when the upperclass were sometimes paying 100x more for their ticket than a third class passenger.
i would imagine there were plenty of other, cheaper ships making the crossing regularly that these people couldve traveled on. So why did the Titanic cater to the lower class at all?
I think you might be confusing the nature of "First Class". Most first class passengers didn't live in luxury suites, they lived in small cabins. First class ticket prices ranged from £30 - £870, a range of thirty fold. At the lower end, you shared a bed in a small-ish cabin with your spouse. The furniture was nice, the food was good, but there wasn't a whole lot more. At the upper end, you got a suite with multiple rooms and your own promenade, with lots of stewards and crew attending to you. There weren't a lot of these parlor suites.
In modern terms, those first class tickets would range from about $3,500 to $100,000. Quite a spread, as you can see.
In contrast, second class fare was about £12 ($1,400 today), while third class tickets ranged from £3 to £8 ($300 to $900 today). In third class, you got a berth in a cabin with 6-8 other people, a sink in the corner. Bathrooms were shared between several cabins, but they did have flushing toilets. Only a couple bathtubs between 700 third class passengers, though.
So as you can see, the difference in ticket prices between first and third class wasn't a hundred fold, it was nearer to 4-10 fold. The 100 fold difference was for the parlor suites, which really shouldn't be called first class. They were a super luxury class way above first.
In terms of economics, third class actually worked out fine for White Star. In fact, they actively advertised it. They realized that most third class passengers were immigrants on one-way trips, not really repeat business, but most immigrants had friends and family who would follow later. So a recommendation from passengers to those who would follow was worth having.
We really shouldn't compare third class prices to modern cruise ships. Modern passengers are tourists, while a lot of the poor on Titanic were immigrants. They had saved for a once in a lifetime trip. It was a huge deal to them, not just entertainment. Of course they were willing to spend more. The return trips were less lucrative, but in 3rd class you'd have immigrants who'd made it in America and saved for years to revisit friends and family left behind.
Yes, Titanic was still more expensive than some other alternatives. There were plenty of cheaper ships. Third class on Titanic was more like second class on other ships. But it offered plenty of amenities for the price. Third class passengers on the Titanic were fed 3 good meals a day. On many cheaper ships, you were expected to bring your own food. The cabins were less crowded, facilities were nicer and cleaner.
So the Titanic didn't attract the bottom rung of third class passengers, it was more the upper end of the working class.
Titanic wasn't a cruise-ship in the modern sense, it was a trans-Atlantic transport, most of the passengers were just trying to get someplace. The Titanic was luxuriously outfitted as well so it was also to some degree an attraction all its own, but like all other ships of its class it was for ferrying people across the Atlantic Ocean. This is very different from modern large ships, which are tourist destinations and designed around recreation not transport.
Interestingly, you can't easily cross the Atlantic by boat as fast as you could in the early 20th century unless you happen to be personal friends with one of the few owners of a record setting superyacht.
Now the fastest and cheapest way to cross the Atlantic is by plane. Anyone who simply needs to get to a destination on the other side of the Atlantic takes a plane. Today you can make such a flight (from London to New York City, for example) for $200-300, which is actually cheaper than a third class berth in the Titanic adjusted for inflation. Even if modern trans-Atlantic cruise ships offered third class berths at similar prices to the Titanic they likely wouldn't be much demand, since the trip can be made cheaper and faster by plane.
Also, only the most luxurious of the Titanic's accommodations cost 100x more than the third-class berths, most of them were about the same spread between "first class" and "coach" that exists today (a factor of a few). The sheer number of 3rd class passengers meant that White Star made about as much money from them as from the 2nd class.
So, to answer your question. Trans-Atlantic ships without third class accommodations would just be leaving money on the table, because there was high demand for such tickets. Most of the passengers at any given time were 3rd class passengers. Attempting to add more 2nd or 1st class berths would have been costly and difficult. The 3rd class rooms were lower in the ship, closer to the boilers where it was hotter and louder. Such spaces were less suitable for 1st and 2nd class rooms regardless of how nice they were made up. Also, adding more 1st and 2nd class passengers would have meant increasing the capacity of the dining halls, adding more crew, etc.
But the more fundamental answer is very simple: the Titanic wasn't full, none of the classes were at full capacity, not even 3rd (though it was closest).