Imagine yourself as a child playing with Legos having as task to build a house.
Now you have a billion ways to achieve that but now few best ways ...
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nice writeup. Please let me point out one subtle issue: Architecture is NOT only the underlying structure, but comprises also technology choices (usually independent of structure), infrastructure topics (deployment etc) and other cross-cutting decisions/concepts.
Proper architecture definitions encompass this somewhat broader understanding (like ISO 42010 and isaqb.org).
In addition, you might want to add another reason/argument PRO software architecture, namely achieving quality requirements like performance, scalability, flexibility, security or even safety. All of these don't just come by good structure or good programming, but need careful thought and usually loads of hard work.
I may point you to a (quite fundamental) series of posts on the same topic (I admit I'm the author...):