In addition to the other issues already mentioned, there are a number of problems when thinking of building an authentic replica of the Titanic. The Titanic was built with the best technology of 1900. It was also an attempt to build a passenger ship larger than any previous examples, with the architects facing new problems for the first time. In retrospect, the Titanic design has a number of known engineering flaws.
They hadn't discovered the bulbous bow at that point, which would make an exact replica very fuel hungry. That was one reason the Titanic's sister ship Olympic was retired, along with other pre-bulbous bow liners, when the 1930's designed liners with bulbous bows like the Queen Mary and Normandie proved to be faster and more fuel efficient.
Titanic was powered by coal fired steam plants. Not very efficient, as compared to modern diesel powered cruise ships or even vintage oil fired liners. Just the labor costs of loading coal into the bunkers and then the massive boilers would be astronomical... labor was much cheaper in 1912, even adjusted for inflation. When ocean liners were built to run on oil, the cost of fueling the ship and operating the ship plunged considerably, as most of the hand labor involved with moving coal was eliminated by simply pumping the oil.
Another basic flaw: there is the danger of coal dust explosions in the huge coal bunkers, when they are nearly empty. It is believed that the Britannic was actually sunk by a coal dust explosion touched off by a single mine, and the Lusitania may have been sunk by a coal dust explosion in a near empty bunker, touched off by a single torpedo... it wasn't the torpedo but a second, much larger explosion that blew part of Lusitania's keel out, sinking it quickly. As Lusitania was near the end of her voyage, most of her coal bunkers would have been empty, and full of highly explosive coal dust.
Another danger of large coal fired ships: In recent years, examination of Titanic photos reveal that the plates that buckled may have been weakened by a fire in a nearly full coal bunker, another hazard of large coal bunkers. It has been theorized, but never proven, that the fire was never fully extinguished, and Titanic was speeding in fog (leading to the collision with the iceberg) to get to New York before the fire flared out of control.
And, an exact replica would reproduce another Titanic flaw... insufficient lifeboats. Both of Titanic's sister ships Britannic and Olympic had much greater lifeboat capacity after the disaster, altering their appearance with the multiple stacked lifeboats on large swinging cranes added to the upper deck.
Not everything is in the blueprints. An examination of the Britannic wreck showed an engineering change made after the Titanic disaster... the flex joint towards the rear of the ship (where Titanic broke apart while on the surface) had been changed on Britannic to a rounded end less prone to cracking and tearing. One has to wonder what other engineering changes were made to correct for errors or lack of knowledge that aren't in the original blueprints. Titanic was very much an experiment in building the largest possible passenger liner... and they didn't get everything right the first time.
Even a lookalike built on modern technology to modern seafaring standards would probably not be practical, once the novelty wore off. Titanic could carry around 2000 passengers. The typical large cruise ship carries three to four times that, while using the same amount of fuel. Tickets for a cruise would be very expensive. Adding enough passenger space to make a repro semi-viable would alter the upper deck lines considerably.
At one point, NCL had purchased the derelict SS United States with the goal of turning it into a cruise ship. The plan was to pull out the aircraft carrier steam turbine engines and replace them with efficient diesels, and add two or three decks to the superstructure to raise passenger capacity (and altering the lines of the ship considerably). NCL found that this simply wasn't economically viable, and that's starting with an existing hull built on 1950's tech, with a superstructure made of aluminum for very light weight (less fuel, higher top speed).
So if a more modern passenger liner can't be converted into a cruise ship economically, it's extremely unlikely that an old design like Titanic could be built from scratch with the expectation of any sort of return on investment. This could be why the current replica in China may have been stalled.