Since the suit became popular as informal clothing in the Western world, starting from the mid-19th to the mid-20th c. Look at old photos from that era and you'll see pretty much everyone wears suit-style clothes in public, even and perhaps especially folks we would consider "lower class" today. There was a reason for that, and it had a lot to do with signaling respect and being considerate to others.
Oh come on, there’s a leap of logic if I ever saw one
It's signalling class, not respect. People can be assholes in any clothes. It's a tool for getting a certain type of person to respect you.
It was not signaling class historically. There's plenty of old photos showing lower-class folks who did wear suit-style clothes, and took pride in what that meant to them. It only devolved into signaling class when basic norms of mutual respect began to be widely connoted as a "middle-class/bourgeois" thing, which started in the mid-20th c. in much of the West and continued to the present day.
Yes, because there are often incentives for lower-class people to signal higher class. That doesn't mean it's not signaling.