Hello, I made the original post and really appreciate the detailed and well thought out responses on here.
I really do very much doubt something like a precise replica would ever be attempted for numerous safety and financial reasons all included in this thread. If there was some eccentric billionaire out there though I think the task of actually constructing a fourth
Olympic Liner would be entirely doable. There's currently 225,000 tonne cruise ships being launched so a 45,000 tonne ocean liner is in the scope of a midsize build. The real expense I imagine would be going for that authenticity, rediscovering riveting techniques, cast molding the engine blocks, all that guild wood carving, etc. If someone had enough money and determination though building an exact replica would not be overly difficult. Getting it onto the ocean with people onboard it would be entirely another matter though.
A lot of responses mentioned that people would be put off by a lack of amenities, cabin size, air conditioning, no hot tub etc. While I completely understand that reasoning I do feel it misses the spirit of a Titanic replica somewhat, if someone wanted to travel in the most luxurious ship possible with all the modern day perks I imagine something like the Queen Mary 2 would be their immediate go to, taking a voyage on her is absolutely something on my bucket list. This Titanic replica however would be marketed towards the adventurous, people with a deep interest in history and obviously primarily those with a deep interest in anything Titanic. Several people mentioned the concept of a floating museum and that is precisely what this would be. There's some amazing photos linked above of some German liner interiors. This whole theoretical venture would be geared for people who want to experience what life was really like onboard a liner of that era. Given how ingrained Titanic is in popular culture, the booming world population and the steady rise of the middle class I genuinely think there could be a profit made in an all out Titanic replica, it would be a completely unique experience.
It was also mentioned a couple of times either fitting out another ship with an Edwardian style interior or making the Titanic a static museum on land, I thought the Truman Show fake voyage was a great idea, it reminded me a ton of the Rick and Morty Titanic episode, minus the sinking simulation aspect. I guess the Chinese Titanic pretty much hits the static attraction nail right on the head although I wish the Titanic Quarter in Belfast had done it first right on the spot where the Olympic class were first built.
I've never been to the Titanic Museum in Missouri but if I ever find myself in that part of the world I'll be sure to look out for it. I was able to stay on the Queen Mary in Long Beach though and spent about four days exploring every bit of her I could access. While the ship has had many changes such as a restaurant now cutting into the promenade I think overall the operators have done a good job of maintaining such a huge ship in as much as possible a historical state. I very much wish I had had the chance to be on a ship like that while she was still on the ocean.
There's been some great comments to on the legal side of things. No port allowing her in is totally valid. Even if you could get Titanic Replica passengers to sign some sort of 'Assumption of risk, release and waiver of liability' ports wouldn't let a 1910's technology liner anywhere near their docks. If she crashed into the dock due to a lack of tugs, azipods, thrusters, etc the onus would probably be as much on the port authorities as it would the Replicas operators. A step around this might be to use the safety escort ship to ferry the passengers to a from the port, much in the way the original Titanic docked outside Cherbourg.
For workers health and safety this is another excellent point. This whole premise is going to the utter extreme of make the replica 100% authentic including a crew stoking the furnaces, etc. This might be an area where a bit of give is necessary such as giving the stokers re-breathers. I don't know if something along the lines of hazard pay would be enough to cover operating on this or would international law ban entirely working on what is effectively a floating death trap with only a nearby ship for support. Another comment mentioned crew diversity, looking at some figures of the original 908 crew 724 of them were from Southampton it would be pretty dubious to hire a predominately white English crew. There's the moral discriminatory aspect not to mention the practical difficulty in finding skilled workers within a single demographic willing to take the job with its unique circumstances. This is an area in my opinion where authenticity again would need to give way to practically and a spirit of inclusiveness.
A last point, I know this is getting long, was disabled passengers. Its a really amazing point and I'm glad Aaron 2016 brought it up. I'm not sure about this, this entire thread is legally way out on a limb as it is. This might again be a situation where authenticity and accuracy bend a little and a couple of cabins are replaced with disabled bathrooms and facilities. In terms of getting around the ship I imagine even in 1912 someone in a wheelchair would have been able to explore much of the ship owing to the continuous flow of rooms and the elevators from A to E deck. If they wished to visit the engine room or boilers though something like that might require assistance from some crew specifically trained to do so in a respectful way.
Anyway I've rambled enough. A warts and all Titanic replica seems like a stretch but really looking forward to the Honor and Glory game being finished, I've always wanted to be able to explore the Titanic and that's probably going to be the best way to do so for a long time yet.