* The equivalent is insurance. Insuring a $2B ship carries pretty good due diligence. A ship simply failing is rare. Of course, ship insurance doesn't care about employee rights, safe food, medical care, or other things one might expect to keep people safe. It's about protecting the capital expense. If everyone on the ship dies, but the ship survives, that's okay!
* Welds are quite strong -- it just extends the metal. This is especially true when the baseline quality of the metal is not high.
On something heat-treated SAE AISI 4130 steel (what e.g. fancy steel bicycles are made of), you see significant weakening. There is a heat-affected zone where the normal tempering is taken off, and the joining material isn't the fancy CrMo of the baseline material.
I'm not a nautical engineer, but I doubt cruise ships are made of overly fancy steel. When you're making a 180,000 ton ship, your best bet is to use cheap steel, and if you need more strength, to simply use more of it. A good weld should be every bit as strong as the cheap steel around it, and the heat-affected zone is a lot less important if the steel isn't heat-treated or tempered in any way in the first place. It will harden the steel a bit, of course, but it shouldn't be the same level of impact.
It's also worth noting you already have welds, and things need to be engineered for welds. It's not hard to reinforce the welds. Indeed, on a bike frame, the welds are where the stresses are highest, and you get around that by making the tubes a bit thicker (or, for fancier bikes, thicker just near the welds -- that's what a butted bike tube does).
I think cruises are horrible, horrible things for a whole slew of reasons, but none having to do with the ship sinking Titanic-style.