Professionals messing with water systems are always well overcosted for the seeming scope of work. The reason being that they need to take out the pan, the walls, some tiles, inspect the floor around the area, remove and replace whatever seems like it’s been damaged, find replacement tiles that are either the same or similar… and the most important part is that they make sure that if they have to come back in 5-30 years for any leaks, they want that to be covered up front as well. You’re effectively paying for leak insurance from them for the next however many years they offer, as well as a potentially brand new bathroom built if the damage is bad enough.

You want a one day fix for a singular part of a greater (and notably damaged) area. They want to make sure they do it once, and then don’t ever hear from you again for that particular part. So there’s all of that and quotes apply Murphy’s Law for unseen issues. The whole floor may need to be replaced, every structural member under the floor might be weakened from excessive water damage and needs either replacement or support, if you have tiles on the walls, some of the walls may need replacement, if there’s an exterior wall involved there they might need to check the those structural members for damage and then possibly replace them, etc. It extends to the whole room and a bit beyond.

I’m going to guess the 16k quote was a “I don’t want to do this, so price multiplied to assure I don’t need to”. My only suggestion is to ask around among others you know if they’ve had work done and by who. There are plenty of freelancers out there who will do exactly the one part you want to do and charge (based on current info) somewhere around 1.5-3k to do just the part of the job you want done, with none of the protections from the larger companies aside from immediate leak issues. Finding a competent freelancer is the toughest part, which is why I always suggest getting one from someone else who has had a good experience (or more).

I got an entirely new shower, rotten floor boards below it replaced, tiles removed and replaced with panels. Switched from electric to mixer shower as well. Less than half that price.

Where I live, 16k gets you a new bathroom. By a contractor.

As the other poster noted, they are quoting you for a lot of maybes.

But also, a big part of the price is simply supply and demand. There is a shortage of experienced, skilled laborers, and it isn’t going away anytime soon. If you are dealing with an independent contractor, for example, your price needs to not only compete against other potential projects in terms of time/effort, but also must compete against the alternative of “what if I just fucked off and hung out with my friends instead?” The beauty of having experience in skilled labor (right now at least) is that your skills are in short supply, but are largely interchangeable with anyone else with the same skills. So if you were to get fired - or just quit because you don’t feel like working - there is no hurry to find another job. You know you can find another job almost instantly. Which is why I know several contractors who just work summers, and then fuck off and go rock climbing the rest of the year.

What kind of building is this? An alpine old house built with rocks and cement? A central european concrete and bricks? A northen european wood house? An american cardboard and framing construction?