There are systems that are impractical to formalize, either because they are too complex, too poorly-understood, too dynamic, too ephemeral, or too expensive to do so.
Your complaints about the words "architecture" and "design" sound like a cached rant. I agree that there's sometimes an uncomfortable amount of squishiness in the way we build technology-systems, but I don't think that's always a bad thing! By and large, we are not specialists in our sciences, we are generalists working in the emergent systems created by the interactions of formal components. For many, this is the exciting part.
We borrow heavily (terminology and patterns) from building, manufacturing, various artistic disciplines, and from complex systems theory. This is inevitable of course -- but when I think of "systems design", I think more of Donella Meadows (Thinking in Systems) than Morris Mano (Computer Systems Architecture, Digital Design) ... though both are brilliant and responsible for hundreds of hours of my university career! (And the latter is a good example of why your objections to terminology are dead ends.)
Our industry builds squishy complex systems (products, applications, interfaces, software, firmware, some hardware) on top of rigid formalized primitives (algorithms, other hardware, physics). The area we inhabit is fertile ground for iteration, agility, and yes, charlatanism. I can understand why that might be bothersome, but I think it goes back to the old vitality-volatility relationship -- can't have one without the other. You may prefer a different part of the curve of course.
I have friends who graduated with Civil Engineering degrees, and work in their industry. Their projects are extremely formal and take decades to realize. This is appropriate!
I have other friends with Architecture degrees (the NAAB, Strength of Materials kind of architecture), who work in their industry. Their projects are a mix of formal and informal processes, and they take years to realize. This is also great.
Now obviously there's a lot of self-selection involved in these groups, but even still everyone has their set of frustrations within their industry. We in technology can iterate in an hour, or a few days for a new prototype PCB rev. This gives the industry amazing abilities, and I would never trade!