Ok I maybe went a little far for the bridge, but today a microprocessor is way more similar to software than it is to a bridge (at least in some of the design phase, but then now even in some maintenance phases). And a modern rocket also contains tons of software. And waterfall is similar enough to (at least non-software -- but in my thesis also software) engineering to even consider a direct equivalent for the bridge. Only, quite like a description of a method is often not enough to see how it is properly used, the mythical "waterfall" where a phase begins after the other one, strictly, never happens, and there are all kind of loopbacks -- even for the bridge -- and obviously if you try to remove loopback things will get fucked-up, but why would you try to do that? Now in real world conversations, waterfall is used to designate software being developed with proper general engineering practices.
Scrum origin is partly in manufacturing. Now there are some common points between some aspects of software dev and manufacturing, especially more so if the software being developed can be iterated very quickly (but very few if it's not the case), but at least in the real world (and maybe even in the theory) Scrum is what is also actually mainly used to interact with other stakeholders. And given how the communication is performed, and its content, that might be better than complete chaos when nobody is actually able to do the work they are supposed to do (PM being limited to having vague ideas, lack of a truly competent tech lead doing actual tech lead work, lack of vision by management, and so over) and only very vague general ideas of what should do the software -- or more generally the whole product -- are ever emitted.
As soon as "serious" stuff starts to be involved, you need real boring engineering, with functional analysis, requirement engineering, modeling, systematic testing or even partial proofs, etc. And you need to have it structuring communication between teams, and day to day work. And then, I don't expect Scrum or anything Agile in such a context adding any kind of value.
Now the theory of Agile and Scrum has evolved because of criticisms to a point where we are told that it actually do not cover the things that matter. That is bullshit retro-justification, now that the world is fucked up trying to make sense how to use that. Here is the Agile manifesto:
> We are uncovering better ways of developing software by doing it and helping others do it. Through this work we have come to value:
> Individuals and interactions over processes and tools
> Working software over comprehensive documentation
> Customer collaboration over contract negotiation
> Responding to change over following a plan
> That is, while there is value in the items on the right, we value the items on the left more.
Engineering is mainly about "processes and tools", of course "individuals and interactions" are also needed, but there is no need to oppose them (although I am not sure what is the point of "individuals" here; the authors might as well said "oh and by the way be nice")
"comprehensive documentation" is critical in all kind of domains, and now that software is everywhere it just makes no sense to declare your "preference" of "working software" above "comprehensive documentation". It is, again, even dangerous to oppose them.
Customer collaboration over contract negotiation; again, highly dependent on the field and specific project if this is something where it makes sense to even have a "preference" or not.
"Following a plan" is what you do about how you organize your work when you use Scrum. There is no problem in studying the impact of a change any time if proper engineering practices are used. Obviously, the cost can vary depending on various factors.
My conclusion about Agile and Scrum, is that if you prefer all of that (4 Agile preferences, and the Scrum theater), you should seek projects that are suitable for the Agile preferences, and so poorly defined that Scrum is a plus. On my side, I'm just not seeking to work on chaotic projects -- on the contrary I try to bring logical and more systematic practice where I feel that chaos reigns -- and I'm neutral about Agile preferences, I prefer to choose projects on other criteria (mostly; intrinsical interest)