The problem is, designing a building, pulling a tooth, or fixing a toilet is relatively easy. There are not so many different ways to do it.
There are actually a lot of different ways to do what you describe, you only think its straightforward because the industry has standardized on methods/tools/etc. Pumbing would be a lot harder if pipe sizes weren't standardized and every plumber around designed a toilet from scratch using tools designed by the guy down the street.
The problem with the computer industry is that lots of times people without a lot of formal training/experience are allowed to create a computer languages, application framework/etc. Those kinds of things are limited to the higher levels of licensing and standardization bodies in most industries. Its this very limit that results in the standardization, not the other way around. You can't even get a Journeyman plumbers license in TX without 4 years work experience as an apprentice.
Frankly, the basics of computer operations tend to be standardized by natural selection, the problems are the fact that there are a million different toolkits (often designed by people without a clue) with a million different bugs/edge cases to bite developers. Plus, a person certified with some level of "web development" wouldn't necessarily be tied to an industry like banking or medical software, especially if there was a higher level industry specific "master" license or some such that would sign off on the work. Its similar to the "architecture" positions in these organizations that are responsible for the design of the system, while the lower level coders do a lot of the grunt work.
In fact the PE licenses for civil/etc work much the same way. Getting a civil PE allows you to work in lots of different industries, but usually there is a senior person with a specialty that signs off on a given project. Freshly minted PE's don't get jobs signing off on large bridges, buildings, etc. Plus, a Civil PE usually will enlist the services of a Electrical PE or Mechanical PE for parts of any given project larger than a tool shed.
So, the problem you describe is a symptom of the lack of licensing not the other way around. Frankly, its only the ease of creation of software that allows this to propagate, any other industry would be hamstrung if it couldn't even depend on something as simple as bolt thread patterns and heads being somewhat standard. Sure programming might not be as exciting if everyone had to learn and prove some level of mastery of Ada but I'm betting there would be fewer stupid mistakes being made by bright people writing an application in languages they have never used before because its the "cool" language du jour.