I'd say there's similar challenges to changing legacy hardware/software and all it interacts with. If all you're doing is new then you could probably devise a robot friendly standard and they'd take over the profession, the issue is the huge variety of how plumbing is implemented within a building of any given age, different building eras in a city, across a country, different countries, complying with all their different sets of regulations, all the variety of parts they connect to. That's with very little plumbing knowledge, in my field of courier shipping where companies have been actively pursuing automation for a long time and still are, even if one of the largest companies with influence like amazon are able to standardize on a few things, it's a huge number of other entities they need to interface with where they are limited on how much they can push (i.e. standard size items) without making themselves irrelevant.

I think they won't replace most household plumbers.

There are many barriers to it happening completely unrelated to the capabilities of robots.

> But the people who will be replaced won’t have money to pay the people with wrenches.

Those people will spend their savings, sell their houses to live in the smaller ones, or find another jobs. They will probably gonna get poorer. But the majority of the people with wrenches definitely will get richer, that is how economy works.