My thoughts on this being a replacement for the Titanic (and later the Britannic II -- come on, now, the Homeric could not properly keep up with the Olympic and Majestic) is that we know that White Star wanted a big replacement ship...
I agree. While I have always been a fan of the Homeric, she was really out of her depth on the three-ship express service, and IMHO the main factor that White Star’s express trio did not quite match Cunard’s service for passenger numbers. As has been remarked upon many times, Homeric’s service speed was designed at 18.5 knots, and although it was supposedly increased by a knot after 1924 she remained slow; the average speed figures for 1923 bear this out:
Majestic: 23.29 knots; Mauretania: 23.29 knots; Leviathan: 23.00 knots; Olympic: 21.44 knots; Berengaria: 20.40 knots; Homeric: 18.11 knots.
In fact, 1923 was a slow year for Olympic, making the White Star trio’s speed differential even starker.
Homeric did earn a degree of popularity, yet I think White Star was disappointed at her passenger lists. While Majestic was more than a match for Berengaria, and Olympic was relatively competitive with the Aquitania, Homeric was no match for the Mauretania’s popularity. In 1922, her debut year, she carried the highest number of passengers she ever would in a single year. Only for three years in the 1920s did she average more than six hundred passengers per crossing, whereas her rival Mauretania was averaging up to eight hundred passengers. In 1923, Majestic’s average passenger lists were more than double Homeric’s. It seems fair to say that Majestic swept the floor with the competition, carrying over 8,000 passengers more than her nearest rival that year, but if it’s unfair to compare Homeric to her then a stark contrast can be made with Olympic. Although it is by no means a like-on-like comparison, by the end of 1920 Olympic had carried more passengers than the Homeric would in her ten years on the Atlantic run from 1922. In 1923, Olympic's average passenger carryings were over forty percent above Homeric's, and she carried over 11,000 more passengers on a heavier schedule. More tellingly, by early 1926 Majestic had been in service for nearly four years, and as the most popular liner afloat for several of those years she had carried as many passengers as the Homeric ever would on the Atlantic.
Broadly speaking, whereas Majestic had up to half of the trio’s yearly passenger share, Olympic had around a third or more and Homeric was left with the remainder. By 1924 her average passenger lists had dropped every year; they began to rise slowly in 1925-26 before the good year of 1927. I think it was quickly clear to White Star that they needed another liner of the Majestic or Olympic’s calibre, and soon after the Homeric had entered service. However, it is easy to be too harsh on the Homeric. As I have said, she was competing on a service for which she was not suited, and had she been on another — secondary — service then it could be argued that she would have been very popular indeed. She would have stood comparison with any of the 'Big Four,' I would wager. She was a fine ship, and it’s sad she did not have the career that she could have enjoyed